Luka Modric’s mind went back to Euro 2008. Everybody’s in Croatia did. The midfielder had blown a 117th-minute penalty to win Sunday night’s World Cup last-16 tie for his country against Denmark and all he could think about was Turkey.

It was the defeat that scarred a generation of Croatian footballers and fans. They had faced Turkey in the quarter-final of the European Championship – it was then the first knockout round – and, when Ivan Klasnic put them 1-0 up in the last minute of extra time, the victory appeared to be theirs.

It had been a dire game, with chances at a premium but, incredibly, Turkey’s Semih Şentürk found an equaliser in the 122nd minute. Croatia were crushed and they would lose the penalty shootout. Modric missed his kick. So did Ivan Rakitic.

It was not easy because the Turkey game was still in our minds. I think it was in everyone’s minds Luka Modric

The parallels with the Denmark game were vivid. In 2008 Croatia had breezed through the group phase, winning each of their three ties, including a 2-1 victory over Germany. They had played some lovely stuff. But against Turkey, they hit the wall. Their cohesion evaporated, together with their spirit of adventure.

Here in Russia, Croatia won all three group games, including a 3-0 thumping of Argentina. Their football was slick, incisive and ruthless. But the Denmark match brought another freeze. What was going on?

There is a further strand to the tale. At Euro 2016 Croatia had taken seven points from an available nine to advance as group winners. They beat Spain 2-1 in the final group match. But against Portugal in the last 16 they did not play. A dismal game was locked at 0-0 in extra time and heading for penalties when Ricardo Quaresma conjured a 117th-minute winner for Portugal.

Since the 1998 World Cup, when Croatia famously reached the semi-final, they had not won a knockout tie at a World Cup or European Championship, an extraordinary statistic given the talent that has been in their ranks. Before Sunday they had not even appeared in another World Cup knockout game and so when Modric saw his weak penalty saved by the Denmark goalkeeper, Kasper Schmeichel, the demons circled and shrieked.

It is almost impossible to imagine the pressure on the players in the shootout, although the Denmark manager, Åge Hareide, offered some insight. “Research has proven during penalty shootouts that your adrenaline and stress levels are as high as when you are in a war zone,” he said.

Modric stepped up to take Croatia’s third penalty, his team trailing 2-1. This time his kick was even softer. He placed it with little conviction down the middle and how his heart must have jumped when Schmeichel, who moved to the left, struck out a trailing leg in an attempt to save. But the ball went in.

Luka Modric after missing his penalty in 2008. Photograph: Clive Mason/Getty Images

Modric had won the most intense of personal battles and his team would do likewise. When Croatia’s goalkeeper, Danijel Subasic, made his third save of the shootout, the scene was set for Rakitic to win it. In another redemption story, a further piece of symmetry, he found the net. Croatia exploded in relief.

“The victory says a lot about our spirit,” Modric said. “I said before the game that since 2008 we had never passed the first knockout game and it was very important for us to take the monkey off our back. And we did it. It was not easy because the Turkey game was still in our minds. I think it was in everyone’s minds because it was so tough for us, that defeat.

“With me missing a penalty in the last few minutes, we needed to have big character and team spirit and everything to stay calm and focused and win the game. With this, I think we can now forget about Turkey. Will it change the mentality? I hope so.”

It should be noted that Modric, after his penalty miss, continued to demand the ball; he did not run or hide. And there was never any question over whether he would take a kick in the shootout.

A monkey off their backs? This was a whole troop of them. The hope is that Croatia, arguably the team of the tournament during the group phase, can rediscover their freedom. Modric has rarely looked so happy after a game and he was all smiles as he spoke to reporters in the mixed zone. Next for Croatia is a quarter-final against Russia on Saturday.

“From the first game of this World Cup, we have showed character and mentality,” Modric said. “And we showed it again against Denmark. This team has character, that is without doubt. But now we need to continue. This team can do much more. Hopefully, we will do.”