The Portuguese former World Player of the Year was responding to comments Mourinho made in an interview over the weekend, taken as a slight towards the forward in the Spanish media.
Mourinho said that aged 30, he had trained 'the true Ronaldo, not the other one, Ronaldo the Brazilian' in his time as assistant at Barcelona.
"Some things in life are not worth commenting on and this is one more for obvious reasons," Ronaldo told a news conference in Los Angeles, where Real are on a pre-season promotional tour.
"I prefer to remember the good things from coaches. I don't spit on the plate from which I eat and I don't speak about people who say bad things about me.
"We are going to face Chelsea, not their coach. It is another warm-up game and we hope to win it so we can start La Liga in the best manner possible."
Real have won all their pre-season warm up games to date under new coach Carlo Ancelotti and take on Chelsea on Wednesday, with Ronaldo having played in a newer more advanced striker role on the pitch.
"The coach has different strategies and different positions for everyone," the 28-year-old said.
"It is good for me to try and play in different positions and I am comfortable with it. We'll see where I end up playing during the season."
Two of the hottest topics surrounding Real in the run up to the start of the new campaign are the club's multi-million euro interest in signing Tottenham Hotspur's Gareth Bale and talks over a contract extension for Ronaldo.
"It's not my place to talk about new players," Ronaldo said when asked about Bale, who according to media reports could eclipse Ronaldo's world record transfer fee of $125 million if the move went ahead.
"It's not my place either to talk about the numbers that are being mentioned for his transfer. I have my opinion but I am not going to say in front of the cameras."
Real president Florentino Perez has said he wants Ronaldo to retire at the Bernabeu, but there appears to be little progress towards extending his current deal which runs until 2015.
"I am happy here and all I want to do is train and prepare well," Ronaldo said. "The contract renewal hasn't been resolved yet, but I shouldn't talk about it because it isn't the right moment."