Dejan Lovren had a message for Slaven Bilic and Igor Stimac – the twin defensive pillars of Croatia’s fabled 1998 team – and it was surely designed to make them smile. “They have a record of reaching the World Cup semi-finals and I want to beat that and I also want to beat them,” the Liverpool centre-half said. “I want people to remember my name in the future, not theirs.”

Lovren has played under the management of Bilic and Stimac for Croatia and he knows how to push their buttons. Perhaps it takes one maverick central defender to know another two. It was put to Lovren that Bilic and Stimac were a little crazy. “Yeah but you need to be crazy in our country,” he replied. “Nobody is normal. I’m not normal.”

Lovren is the loose cannon in the Croatia artillery; self-assured, direct, larger than life, but he is a part of a blend that has come together at precisely the right time. Rewind to October last year and Croatia were in crisis after drawing their penultimate qualifying tie at home to Finland.

They sat joint second in the table with Ukraine and the final fixture was against them in Kiev. Lose and they were out. The Croatian Football Federation took decisive action, sacking the manager Ante Cacic and replacing him with Zlatko Dalic. Everything rested on Dalic finding the answers – and fast.

How he has done so. Dalic’s team won 2-0 to set up a play-off against Greece, which they won 4-1 on aggregate and, after four warm-up games, they have taken the World Cup by storm.

They beat Iceland at the Rostov Arena on Tuesday in a game they did not need to win and, frankly, one they did not look as though they wanted to win in the first half. With qualification to the last 16 assured and a much-changed lineup, they found the extra gears after half-time to dig out a 2-1 victory.

There is a ruthlessness about Croatia, not to mention a depth to the squad. Dalic had started with only two of his first-choices against Iceland: Luka Modric and Ivan Perisic.

It is pretty much the same group who had laboured under Cacic so what has changed? Lovren puts the upturn down to better chemistry. Croatia have talent, they have always had talent – players at top clubs across Europe. But Dalic, who was recruited from Al Ain – he had managed in the Middle East for the previous seven years – has instilled togetherness.

“I see a difference between this squad and the one that went to Euro 2016, definitely,” Lovren said. “I feel it’s totally different. It has not changed over the two years – maybe just in the last games when the manager came in. I had a good feeling from the beginning. I’ve felt something, on the pitch, outside the pitch. It’s this strong commitment to each other. You feel it when you talk to the players.

“The manager has his own ideas. He has brought in something new and if he tells you he believes in you – it’s like in all sports – you will start to believe in yourself and with that comes the atmosphere and the people around. It’s amazing.”

It should be said Lovren did not see eye to eye with Cacic and there has long been the potential for flare-ups within the Croatia setup. They are playing with 22 players in Russia, after Dalic sent home the striker Nikola Kalinic. He had refused to come on as a late substitute in the opening game against Nigeria, which Croatia won 2-0.

Their belief has soared – fired, in particular, by the 3-0 thumping of Argentina – and, for the first time since 1998, they have advanced into the knockout phase, where they face Denmark in the last 16 on Sunday.

The Class of 98 shadow the squad. It feels as though every time Dalic and his players stand in front of a microphone they are asked about Davor Suker, Zvonimir Boban and the glory boys from a time now past but who are still keenly felt. Back then, Croatia were a newly formed nation and, at their first finals, they swept past Romania in the last 16 and Germany in the quarter-finals before falling to France.

“I turned nine during the tournament and I remember it clearly,” Lovren said. “I remember my mum screaming in the house when we scored. Afterwards, I knew that third place was a big result.”

The line from Lovren is that the squad can and will emulate them, and that they might even go one step further and reach the final. “We can beat it, definitely, but we need luck,” he said.

There is an omen, of sorts, on Croatia’s side. In qualification for 1998, the team beat Ukraine in a play-off, which is effectively what they did this time. But Lovren is focused only on Denmark.

“We are definitely the favourites against Denmark but they passed a tough group, although it was not as difficult as ours,” he said. “It will be difficult. We have played against similar teams to them – Sweden, Norway. These Scandinavians teams, they all have similar styles so we know how to play against them.”