Odsonne Edouard netted the only goal of the game eight minutes into the contest with a strike from the edge of the area which found the back of the net via a massive deflection off Dons defender Tommie Hoban.
The goal came against the run of play in the early exchanges with Aberdeen having two early chances to take the lead. But while they had a brief period of sustained pressure in the second period, they didn’t do enough to threaten the Celtic goal the rest of the way.
Still, McInnes felt his team were hard done by at the home of the reigning Scottish champions.
He told BBC Sportsound: “It was similar to last Wednesday – a moment of quality beat us last week – and a real moment of luck today.
“I think it’s harsh on us the scoreline, I thought we started the game well with plenty of impetus in our play. We had two very good chances, Ash [Taylor] should probably do better with the second one, but [Scott] Bain makes a good save.
“I thought we were on the front foot, proactive with our work and we asked the question initially. Then we lost the goal and I thought we lost a degree of confidence from that.
“In the first half Joe (Lewis) hasn’t had any else to do apart from pick the ball out of the net. To that extent we were comfortable enough, but being a goal down the onus was on us to get after them.
“People think it’s just our pressing and out of possession work, but we have to keep the ball better. Too often the balls into strikers weren’t kept and that allows you to get up the pitch and allows you to play where you want to play as we did second half.
“We put so much into it and I’m pleased with the performance, but I’m frustrated and annoyed that we haven’t got anything from it."