Andy Carroll's header four minutes from time sealed the win for Kenny Dalglish's side.
"I take full responsibility for that goal. I think it changed the game, so I have to accept it," Distin said.
"[The players] don't need to point at me or anything because they know I'm man enough to face my responsibilities.
"That's clearly a bad mistake from me and I have to accept it, no matter the consequences. And, for me, the consequences are not going to the final, which is very disappointing."
Distin went over to the Everton fans after the match to apologise for his costly blunder.