The Dons, who knocked Celtic out of the Scottish Cup at Parkhead two weeks ago, inflicted a first league defeat of the season on the hapless Hoops.
Goals from Jonny Hayes and Adam Rooney put Aberdeen 2-0 up at half-time before James Forrest pulled a 61st-minute goal back for the champions, who had been unbeaten in their previous 26 league games this season.
McInnes said: "The fans have seen their team win and deservedly win with two magnificent goals and loads of effort from every single one of the players.
"It's not easy beating Celtic whether it's against 11 men or 10 men.
"You can see why these players play for Celtic, they never know they're beat. I thought they took full responsibility in the second half and the introduction of Forrest caused us problems.
"We were too deep and it was a bit disappointing that we never kept the ball better. When Celtic score it adds to the anxiety in the ground and belief of Celtic.
"But over the 90 minutes I thought we were the better side and created the better opportunities."