The Ivory Coast striker was sent off in the 117th minute after slapping the United defender.
Drogba said: “I have seen the match on video and I believe I should not have been sent off with three minutes to go.
“If I had punched him, I would have understood. Now I wish I had.”
He added: “You have a lot of regrets when you go to the final and lose it.
“I have more regrets about losing the final than being sent off.
“The team was affected by the sending off and we lost on penalties.
“But it wasn’t the worst feeling. Hitting the post was. I wasn’t feeling well because I was playing alone and against world-class defenders.
“When you get a chance like that you have to take it.
“Some Chelsea fans blame me for losing. I can take it but I think I gave my best, as I always do, because I want to be No.1. Sometimes I want that too much.
“I apologised to my friends. People can make mistakes.”
