The veteran centre, who was on his fourth Lions tour, played in the first two Tests but was left out of the match squad for the 41-16 victory as coach Gatland opted for the Welsh pair of Jonathan Davies and Jamie Roberts.
The decision caused a storm of controversy, with New Zealander Gatland accused by former players of failing to understand the Lions, while O'Driscoll said that two months later he was still upset at what happened.
"Do I resent him? Yeah, there's resentment of course," he told Sky Sports. "Is he on the Christmas card list - unlikely.
"When you're left with disappointment that way, you can't but feel a little bit of resentment you know."
Davies and Roberts performed strongly as the Lions sealed their first series win since the trip to South Africa in 1997, but O'Driscoll, who had earlier said he had not been dropped since he was 17, believed he could have done just as well.
"People will say the decision was justified because of the results and the performance I guess.
"The way the team played I felt within the 13 jersey that I might have been able to do a decent job within that part of the team the way they played in that game.
"That's absolutely not taking anything away from Jonathan's performance, I thought he was pretty good that day, made some big plays at important times.
"But I guess it comes back to you backing yourself, feeling you too could have done some things that maybe others didn't do on the day."
The 34-year-old also revealed this week that he plans to retire after the upcoming season.
He signed a one-year contract extension earlier this year, but told the Irish radio station Newstalk that this would be his final season with Leinster and Ireland.
"This is the 'one more year'. I had to think long and hard (about playing an extra season) and there were a number of factors.
"I had to talk to (wife) Amy and listen to my body, I had to learn if I was still wanted in the Leinster set-up and the Irish set-up."
Meanwhile, Davies said he considered himself "public enemy No 1" after the outcry, and talked to scrum-half Mike Phillips, who had received flak himself for off-field incidents, on how to deal with it.
Despite the controversy, he still celebrated the win with O'Driscoll.
"Obviously he was gutted not to be involved but the way he trained over the next couple of days was testament to the guy.
"Before the test he didn't say much, he just let me get on with it. We had a couple of beers together after the Test, we got on fine."
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