The world's most expensive player scored both goals for Real Madrid in their 2-0 home win, moving them to within five points of leaders Barcelona.
But he picked up a red card in the 70th minute after swinging his arm behind him and catching Mtiliga in the face as he tried to spin away from the Danish defender's clutches.
"People who understand football know that my intention is always to try and play. The red card is a disgrace I don't understand it," Ronaldo told reporters.
"I've been down to the Malaga dressing room to apologise and he understood the situation. I know you saw blood on the TV screens but I was just trying to break free. I never try to hurt anyone."
Malaga coach Juan Ramon Lopez Muniz said Mtiliga had broken his nose and would be out of action for around three weeks.
The Andalusian club's president Fernando Sanz was critical of Ronaldo's attitude when he was interviewed immediately after the game.
BRUTAL IMPACT
"I don't suppose Ronaldo meant to do it but he swung his arm back once and the second time he did it he broke the player's nose," Sanz told Canal Plus television.
"It was a brutal impact and a clear sending-off offence. What he should have done is left the field apologising to his opponent rather than throwing his arms in the air and protesting."
Real Madrid coach Manuel Pellegrini said he was unable to see the incident clearly but the club's director general Jorge Valdano rushed his player's defence.
"The referee has to understand which players want to entertain and those who want to break up the spectacle," he said.
"Cristiano wants to play (football). When a player grabs him from behind he tries to break away from them. Others throw themselves to the ground to simulate a foul.
"More than Ronaldo's need to adapt to the Spanish league the referees need to adapt to protect players who want to entertain.
"I don't want to judge referees decisions, simply to state that Ronaldo's intentions are always noble."
It was Ronaldo's second red card for Real Madrid after being sent off in a league match against Almeria last month.
