The London club stifled Liverpool's much-vaunted attacking threat on Sunday, scoring at the end of each half through Demba Ba and Willian in a 2-0 win that lifted Chelsea to within two points of the Premier League leaders.
Rodgers, who got his big break in coaching as an assistant to Mourinho, was critical of Chelsea's tactics in the aftermath of Sunday's game but Mourinho said on Tuesday it was all water under the bridge.
"Brendan is somebody I consider my friend. Of course I know his words after the match but I also know his words today. Today he told me: 'Congratulations for a great victory and a great performance'," Mourinho was quoted as saying on Chelsea's official website.
"Especially because he is somebody I consider a friend, and I like, I prefer to forget the words after the match and keep the words of today.
"He's an intelligent guy and I believe that after the match he watched it on video and now he understands what happened."
Chelsea also delivered a dogged defensive performance in Madrid last Tuesday to hold Atletico to a goalless draw in the first leg of their Champions League semi-final.
Mourinho said defending would also be crucial in the second leg at Stamford Bridge on Wednesday.
"The team that doesn't defend well doesn't have many chances to win," he added. "The team that doesn't score a lot of goals - and if they also concede a lot of goals - is in trouble. A team without balance is not a team.
"When Atletico have the ball we have to defend, when we have the ball we have to attack. This is the football that I know.
"When a team plays strategically, and thinks about the qualities of the team and the qualities of the opponent, 10 or 20 or 30 years ago they are a good, intelligent team.
"In this moment, depending on the coach and the club obviously, the critics speak but that is no problem." (Writing by Peter Rutherford: Editing by Nick Mulvenney)