The QPR board took the decision to part company with Warnock following a string of negative results that left the club one place above the relegation zone.
Rodgers, who achieved promotion with his club along with the 63-year-old last season, believes that Warnock's experience will help him deal with his dismissal.
"Obviously I have empathy for Neil and it is always sad when any manager loses their job," Rodgers told Sky Sports News.
"Like I say, he's been around the block and he knows exactly how to deal with these situations but they're never nice of course when they come along.
"But Neil is a terrific manager and I'm sure he'll bounce back once he has a little breather with his family."
Rodgers recently went head-to-head with Warnock and QPR, with the match ending 1-1.