Mateo Kovacic believes two "cardinal mistakes" from referee Daniele Orsato cost Croatia in Tuesday's World Cup semi-final defeat against Argentina.

Croatia's bid to reach a second consecutive World Cup final came to an end as Lionel Messi and Julian Alvarez starred at Lusail Stadium, with the latter scoring twice in Argentina's 3-0 win.

Messi opened the scoring from the penalty spot after Alvarez collided with goalkeeper Dominik Livakovic, and Kovacic was booked for dissent as several Croatia players protested the decision.

Less than a minute before Livakovic's foul, Croatia were denied a corner when Ivan Perisic's deflected shot looped onto the roof of Emiliano Martinez's net, leaving Kovacic in disbelief. 

"I can't believe it's not a corner," the Chelsea midfielder told reporters after the game. "Then the penalty... 

"I have never commented on the referees nor is it my intention to do so, but these are two cardinal mistakes, and they cost you."

Kovacic's midfield partner Luka Modric concurred, insisting Croatia were in the ascendency before the penalty was awarded.

"The first goal, it was not a penalty, that's my opinion. It stressed us a little bit. Half a minute before that it was supposed to be a corner and we were not awarded one," he said.

"I think after the penalty, it changed the whole match. Before the penalty, we were the ones controlling the game. 

"Maybe we were not so dangerous in front of their goal, but we were the ones in possession, controlling the ball. 

"Unfortunately the penalty changed everything, a penalty I'd never have called in this match. I'm so upset they called this type of penalty against us."

However, Modric did acknowledge Argentina were deserved victors, adding: "We lost the game, that happens. We just have to congratulate Argentina. They were the better team today, they for sure deserved it more than us."

Meanwhile, Kovacic credited Messi for another outstanding performance as the 35-year-old became the first player to both score and assist in four separate World Cup games.

Messi teed up Alvarez for his second goal after beating Josko Gvardiol twice in the same move, while the Manchester City forward's first strike came at the end of his own impressive solo run.

"We knew they were aggressive and good and that they had Messi," Kovacic said. "He was phenomenal and should be congratulated.

"Those two situations are incredible, we conceded two ridiculous goals."