The hosts kept alive their hopes of winning the title with a 3-0 win, thanks to goals from Antoine Semenyo, Omar Marmoush and Savinho, a result that keeps Palace 15th with two games left to play in the Premier League.
Glasner's side did have their moments and would have taken the lead in the opening minutes, were it not for a marginal offside ruling against Brennan Johnson.
But the Manager said that Palace should have used the ball better after that early glimpse of the City goal.
"I think today we have to accept City were much better than we were," he said in his post-match press conference. "If you want to get a point or maybe more, at the Etihad, you have to deliver a top performance.
"The second-half was a bit better. We had a few moments to come back. But today we were not on our best level and that's why we lost.
"I think in possession we moved the ball too slow. We didn't really stick to the plan in possession. We did once and this was the offside goal.
"We needed the runs, but you can't go straight in behind. You need to prepare it. In preparation, we were too slow.