Chelsea won 2-0 to keep their slim title prospects alive and dent Liverpool's hopes of winning a first championship in 24 years.
"You know pundits are pundits and I don't want to comment a lot," Mourinho said.
"Brendan is a manager and is somebody that I consider my friend.
"I met him a long time ago when he was a very young coach coaching kids.
"Of course, I know his words after the match but I also know his words today and today he told me congratulations for a great victory and a great performance.
"Especially because he's somebody I consider a friend and I like, I prefer to forget the words after the match and I keep the words of today.
"He's an intelligent guy, I believe that after the match he watched the match on video and I think now he understood what happened."