Ronaldo struck the first goal of his memorable hat-trick to put Portugal ahead in the fourth minute after going down in the area from a challenge from Nacho. He later converted an exquisite late free-kick to level the thrilling encounter after winning a foul following a tussle with Barcelona's Pique.
"Cristiano is very prone to diving and they award him almost every foul," Pique told reporters after the extraordinary spectacle in Sochi between the two heavyweights which set the World Cup alight.
"We picked ourselves up again after a lot of problems because starting a World Cup by conceding a penalty in the second minute and going behind is difficult but we scored three goals and we have to be happy with how the game went."
Spain's ability to come back in the game after Ronaldo's first two goals was all the more impressive given the turmoil that had gripped the team after Lopetegui was sacked on Wednesday for negotiating a move to Real Madrid behind the back of Spanish Football Federation president Luis Rubiales.
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Pique, who is famous for his open disliking for Barca's arch-rivals Madrid, said now was not the time to analyse whether it was right or wrong to dismiss Lopetegui but hinted he disagreed with his former coach's methods in the negotiations.
"We all have to pull together now, it's a situation that no-one has enjoyed but the World Cup has started, and when it's over that's when we can tell the story, we need to speak as little as possible and focus on football," Pique said.
"The fact he negotiated with Madrid doesn't bother me, a huge club came for him, the way he did it is up for debate. There are thousands of opinions, the president didn't like it and took his decision and the players have accepted it."
Spain striker Diego Costa produced an explosive performance and pledged to "keep working and keep on shutting people up" after his two goals answered critics who believe he does not fit into the team's style of play.
The Atletico Madrid forward also declared his admiration for Ronaldo after the Portuguese upstaged his two goals with his whirlwind hat-trick.
"There will always be a debate, that's good as it means there is competition in the team," Costa said.
"I have to congratulate Cristiano, they criticise him and just look at what he does. People would be better off leaving him alone. I wish I was like him."
(Reporting by Richard Martin; Editing by Amlan Chakraborty)
