The pair clashed after Real's victory over Barca on Saturday and Modric was asked about Pique's complaints in his Champions League presser.
He responded: "What is said from outside cannot stain our history, what we are doing. There are always many complaints against us but when you are the best team in the world it is normal for that to happen.
"What is said from the outside and the criticisms cannot tarnish our image at all. No way."
Asked about talk of a move for PSG striker Kylian Mbappe, Modric also said: "I do not know what to say. There is a lot of news about which players are going to come or those who are going to leave. I can't get into that. Speaking of Kylian, he is a great player and he has shown it in France and PSG. Great players are always welcome at Real Madrid. It would not be correct to talk about players from other teams at this time of the season. Let's see what happens next year."