Croatia goalkeeper Dominik Livakovic was rightly hailed after his team's stunning World Cup quarter-final win over Brazil, but their midfield trio were also crucial.

Luka Modric, Mateo Kovacic and Marcelo Brozovic helped Croatia earn a 1-1 draw with the record five-time winners after 120 minutes, with the European side triumphing 4-2 on penalties.

Even though Brazil had by far the more dangerous openings, with 11 shots on target to Croatia's one, possession was split evenly.

Croatia's midfield was able to help them keep the ball for an hour of the game, stopping the likes of Neymar, Vinicius Junior and Raphinha racking up even more opportunities.

"I said several times that Croatia has the best midfield in the world," proud coach Zlatko Dalic told a press conference after Friday's game.

"We can pass the ball, control the game and control the ball, we did that today. Our midfielders were not hasty, that was the most important part.

"I believe the midfield is the best part of our team, they [kept] possession and blocked our opponents."

Celtic right-back Josip Juranovic, who also put in a fine display in the win over Brazil at the Education City Stadium, agreed with his coach.

"We believe in ourselves -- I can say we have the best midfielders ever," said Juranovic.

"Brozovic, Modric and Kovacic -- if they are in the game I think that we will control the game 90 per cent and because of that I think that we beat [Brazil]."

The trio have been essential, starting every game at the tournament and helping to protect Croatia's defence, which has conceded just two goals.

No stars

By not dropping too deep Croatia's midfielders give the team some breathing room, possessing the wherewithal to confidently keep possession further up the pitch.

They are one of the reasons a nation of just four million can consistently compete with the world's strongest teams.

When they finished runners-up in 2018 it was with Ivan Rakitic in the side, but Kovacic has stepped into his shoes.

Inter Milan's Brozovic plays the deepest of the trio and never allowed Brazil to be comfortable, while Chelsea's Kovacic is highly mobile and always offering options.

However it is Real Madrid midfielder Modric, 37, who earned special praise, both for his quality and his longevity.

Modric also stepped up in the shootout, sending Brazil goalkeeper Alisson Becker the wrong way with a coolly-taken spot-kick.

"Again Luka led for 120 mins (at) a great rhythm and took the penalty when he needed to," said Dalic.

"It's unbelievable how he plays. He is not tired, he didn't fall behind, he played the whole 120 minutes.

"At 37 years of age it is unbelievable but that is Luka Modric and it shows he is one of the best players in the world."

Croatia defender Borna Sosa went further, saying Modric was one of the top five midfielders of all time.

"Nobody, absolutely nobody performed on his level at 37 years old, and he's showing from year to year how important of a player he is for us and Real Madrid," said the full-back.

With a semi-final against Lionel Messi's Argentina beckoning on Tuesday, Croatia must rest and recover, because they will be required to give every ounce of sweat again.

That resilience and determination is a key part of their game and would not be possible if players like Modric did not give their all, despite his status as a Ballon d'Or winner.

"Our biggest strength as a team is to fight together and to not have stars in the team who don't want to run, or defend," added Sosa.

"We don't have 25 players who are playing at Barcelona, Real (Madrid), so we have to be ready, everybody.

"Luka Modric is playing every game because he has to. There is no place for him to rest, because we need him every second on the pitch."