Drogba broke the deadlock in the 68th minute - his fifth goal at Wembley - before two goals in the final two minutes from Florent Malouda and Frank Lampard sealed the win.
"I always say I'm lucky, it's an honour for me to be here and to play in a stadium like this one," Drogba told ITV.
"The FA Cup is really special to us and when I have the chance I will try to score. I had two chances before and I was a bit unlucky, the first one was a great block from (Stephen) Warnock and the third chance maybe was the one that was least expected, but that's the goal."
Drogba started Chelsea's critical Barclays Premier League clash with title rivals Manchester United on the bench last week before coming on to score the winner, but insisted not starting was not a problem for him as Chelsea compete on multiple fronts.
"I've been in this position before, I know why I was not starting, it's not a problem," he said.
"The objective is to win the game. We have six games left to go with the final and we have to win them all."