Mourinho, who admitted to missing the goal due to a discussion with fourth official Phil Dowd, appeared to be involved in a row on the touchline with Liverpool counterpart Rodgers during a fiery second half.
The Portuguese described himself and Rodgers as "very different people".
Mourinho added: "He worked in Chelsea in my time for a few years. I don't know if he learned something with me or not. Maybe he did, maybe he didn't.
"I could speak about Skrtel, I don't. He goes to the television, he speaks about (Chelsea keeper Thibaut) Courtois. He forgets (Liverpool keeper Simon) Mignolet. I speak about Courtois and Mignolet.
"He forgets his goalkeeper. I don't forget my goalkeeper, because my goalkeeper helped me to be in the final.
"He is what he is. He is a fantastic manager, but we are different people."
But the Liverpool boss said: "There is no problem. It's a competitive game between two top sides and the chimp comes out every now and then."