Derek McInnes praised Aberdeen for learning lessons from their previous Celtic Park visit after knocking the holders out of the Scottish Cup.
and reach the quarter-finals.
"A few months back, it was 1-1 and we missed a couple of opportunities to get ourselves in front and we ended up losing the game," McInnes explained.
"When today's game was finely poised at 1-1, it was Aberdeen that got the winner and that pleases me no end.
After Anthony Stokes's early opener for Celtic, Russell Anderson volleyed Aberdeen level and Peter Pawlett's second-half strike proved to be the winner.
"I'm delighted for every one of our supporters that's come here," McInnes reflected.
"We've had a few sore ones over the years and it's been a long time since we've managed to get a victory here.
"Today was a proper team performance. It wasn't about individuals.
"The platform's all about denying them space, never being stretched.
"People will talk about maybe Celtic's failings and maybe they fell short at times and they've got a bit more quality to show than that but I do feel that we played a part in that.
"It's a great result."
Aberdeen remain in the hunt for a domestic cup double, having already reached the final of the League Cup.
"We, at the minute, have just got ourselves in the fight," added the Dons boss.
"We've got to respect Inverness because they can stop us. They've got the same chance as us of winning the League Cup.
"And there's another seven teams that will be in the Scottish Cup draw along with us. They will all be dreaming of what we're dreaming of, that we can win another cup.
"We'll still get success, hopefully, in the league through the European slots.
"We're just glad to be in the fight. It's been a long time since being able to say that as a club and long may it continue."