One by one they got up, the pile of bodies peeling away a player at a time until there were only two remaining and the Atlético Madrid captain, Gabi Fernández, lifted Diego Godín to his feet, then left him there. Taking a step back as if dizzy, the man who had laid at the bottom pulled his shirt to his mouth before heading to the centre where cameras catch a lost, stunned look, like he can’t take it in. Stop the tape and you can see the moment he tries to snap himself out of it. It was the final day of the 2013-2014 season and it was actually happening – if they could hang on for 40 minutes more.

“We were losing at the Camp Nou against Barcelona, and the league was slipping away – a league we’d fought so hard for, over 38 games. It had taken so much from us, and you knew that in one game all that work could be gone. We were losing, Diego Costa had got injured, Arda Turan had got injured, and everything was uphill,” Godín recalls. All year, people had said Atlético Madrid would fall away and, he admits, they “fed” on that, rebelling, but now they were falling at the last. And then, he scored the biggest goal in their history to ultimately earn a 1-1 draw, and the title.

“We knew it was back in our hands and there was a relief; you feel your body filling again,” he says. “At the end, you let go: all the happiness and tension. There had been a huge buildup of emotion all year, it had been hard, intense, and for that goal to have give us the title was incredible.”

That is one word for it. Diego Simeone, the coach, had called it “impossible”, thus proving that nothing is. When Atlético became La Liga champions, he took the microphone during celebrations, a quarter of a million people on the Madrid streets, and made it a lesson in life. “This is not just a league,” he said, “what this triumph transmits is much more than that: if you believe and work, you can do it.” There had been applause from the Camp Nou. Although Barcelona had been defeated, it was something to recognise and be thankful for – almost as if this was everyone’s title.

Two years later, it happened again. Sitting in the stands at Atlético’s Cerro de Espino training ground, 20km northwest of Madrid, Godín says: “I was really pleased and I think the immense majority of football lovers, fans everywhere, would have felt the same way. To see a small, modest team built on hard work, where the players are so close, so together, win week after week, stay up there and play so well, when they’re so consistent and they win the league, that makes people take them to their hearts.”

To see a small, modest team built on hard work win the league makes people take them to their hearts

He is not talking about Atlético, although he could be; he is talking about Leicester City. “Personally, I think it’s wonderful,” Godín says. “I’m sure lots of people would have fallen in love with Leicester a bit. It makes you happy things like that can happen in football.”

Godín, a fan who admits to being enamoured with the game, an obsessive watching endless matches, did not just enjoy Leicester winning the league; he identified with it. One of the recurring themes of this quarter-final is the sense that these teams share something. Atlético Madrid did a Leicester before Leicester did. There was even a parallel with their last goal before being Champions, two centre-backs scoring at the biggest ground in the country: Wes Morgan at Old Trafford, Diego Godín at the Camp Nou.

True, Atlético’s title was their 10th, not the first, but it really might have been the most impressive in Spanish history. It was never a target, Godín admits, and it wasn’t until they beat Athletic Bilbao in late March that Simeone even thought it possible, although Godín places it a sooner, saying: “we started to believe around February”. And even then, a last minute save from Málaga’s Willy Caballero denied them on the penultimate weekend, obliging them to go to the Camp Nou and take the title from Barcelona. Just as the season before they had to beat Madrid in the Copa del Rey final – at the Santiago Bernabéu.

Diego Godín is congratulated by his Atlético Madrid team-mates after his equaliser against Barcelona that won the Spanish title at the Camp Nou in 2014 Photograph: Marcelo del Pozo/Reuters

They were up against the most fearful of opponents, although they love to rebel. Godín does, too: he was born into it. It is not just Leicester that Atlético are similar to; it is home. There is something in the national psyche or its place, visible on a map. “There is a parallel with Uruguay: in the middle of two great powers, and not just in football terms, but world terms,” he says. “We’re a small country, with few players, few resources, only three million people, that has always rebelled and done big things in football – against the great powers.”

Atlético faced the greatest of them all. Their budget was barely a fifth the size, well over 400m between them and Madrid or Barcelona; it was 18 years since they won the league; no one outside Madrid and Barcelona had taken the title in a decade; and for the previous five years the nearest anyone else had got was 17 points. And there was something else too, Godín notes: six days later, they had to play the Champions League final, against Real.

“It is grandísimo what Leicester did, absolutely enormous,” he says. “But what we did, winning a league above Madrid and Barcelona in this day and age, is very big. Leicester were a very consistent team that took advantage of other teams’ inconsistencies. We won an impressive league and reached the Champions League final, which I guess makes it even more of an achievement; we had to keep winning and at the same time keep going through Champions League rounds, against very good teams.”

They have kept doing so since. This is a one-off for Leicester; it is the fourth season in a row that Atlético are in the Champions League quarter-finals; they are seeking their third final in four years. Even more than a rebellion, it is a revolution – small wonder Gazetta dello Sport mocked up Simeone as Che Guevara. When he arrived, they were 10th and they had been beaten by a Second Division B team in the Cup. Their captain said they were “sunk”, but they won a Europa League, then the Copa del Rey, then La Liga. Here they are again: it feels natural now, the idea would have been laughable then.

“We couldn’t find a way to win, which is why he came,” Godín says. “And in those first six months, we improved, we built the structure, the core that’s made us so strong. We won the Europa League and had to row and row to try to make the Champions League. We missed out, just, but that provided the basis for the next season – and it went from there.”

But how?

“Simeone came to a place he fitted perfectly, where he was loved and had a huge amount of moral authority. Some people fit certain places: his place was Atlético,” Godín says. “He found a group of players who were waiting [for him], who wanted to rebel. It was an accumulation of things. Beyond the mental question, vital in any walk of life, there’s no great mystery: there’s a huge amount of work behind this team. We’ve been together for over five years, and that shows. What we have done is not chance.”

“When you have a team that works like this and a coach everyone believes in, who they follow, when you have this momentum, a great environment around the team, success follows. The values of sport are a reality: effort, sacrifice, work. Sure, everyone says that, but it is true. We’ve created a positive wave.”

“There’s a huge amount of tactical work, a lot of individual work, and everything is conditioned by the way we play and what each player needs physically. Barcelona won’t train like us. There are a thousand tiny details, a throw-in, a corner, a free kick from the side, every scenario.”

So, little improvisation, then?

“Very little improvisation.”

“Bear in mind, too, that we have been together for a long time now, there are so many hours of work under our belts that some things no longer need to be worked on. We’ve assimilated ideas so completely that there are things that we don’t even need to repeat.”

That allows for continuity, even if new players have had to get used to new approaches: there’s almost something sadistic in the amusement felt when new arrivals struggle through the summer, but it works. Departures haven’t sunk them. “When you look at it the most decisive, most important players – the strikers – have left us each year,” Godín says. “Cholo has been able to reinvent the team. He’s brought a kid like Antoine Griezmann from Real Sociedad who would score a goal one week then go maybe three without and now he’s one of the best three players in the world, competing for the golden boot, great consistency.”

Jamie Vardy of Leicester City challenges Diego Godín during Atletico Madrid’s 1-0 victory in the Champions League quarter-final first leg in Madrid. Photograph: Michael Regan/Getty Images

And taking Atlético a step closer, his penalty and a superb performance in last week’s first leg giving them a slim but significant lead. Here they are again, 90 minutes from another semi-final, against the team in which they see themselves reflected and players they could imagine playing alongside. Jamie Vardy, say? “He would fit in at the vast majority of teams in the world,” Godín says. “He works, sacrifices himself for the team, and on top of that scores goals. Who wouldn’t want a striker who kills himself for you, then gives you attacking solutions?”

“A striker like that is fundamental for a team like Leicester that plays the way that they do. If they didn’t have that kind of striker, maybe they wouldn’t be Leicester, the team we’ve seen,” he continues. “He’s a great player, who fights and competes. Against Sevilla [in the last 16], every ball that went into the Sevilla half he fought for: he never gave a ball up for lost. At the Calderón he was virtually alone and if he didn’t touch the ball often that doesn’t mean he’s not a great striker, quite the opposite. It’s because we paid him so much attention. We were focused on not giving him space, cutting off access to him.

“The first leg confirmed what we knew: that Leicester are a team that shows solidarity and commitment, that works extremely hard collectively. A measure of that is that we dominated the game but it was hard to create many clear chances, so we’re happy to have been able to win. In a two-legged tie it’s always important not to concede; we have to make that count in England.”

A semi-final awaits the other side and, beyond that, the final. And there’s the rub, the thorn buried deep in their sides. That day at the Camp Nou, Godín scored the most important goal in Atlético’s history. He might have surpassed it six days later when he scored in Lisbon, his header taking them to within seconds of a first European Cup before Sergio Ramos appeared in the 93rd minute. Two years after that, they were denied on penalties by Real again. It proved a rebellion too far, even for them. Simeone likened the weeks after Lisbon to “a period of mourning”. But they came back, and back again, as if driven by defeat.

“Look,” Godín says, “no one likes to lose – and still less the way that we lost. Of course. We’re not going to hide, we’re not going to lie. But we’re not taking this as revenge and nor do we think we have to win it because of that. No. We have the same desire to win the Champions League, the same ilusión as ever. This is the biggest dream we have and we’re going to fight for it.

“We’re among the best eight again, which isn’t easy. It’s very hard to win the Champions League but we know how; we know the path we have to follow.”