Aberdeen, pressing high and bristling with enterprise, held the edge over their lacklustre hosts for the bulk of the opening period but Jason Denayer's header from a corner kick meant it was 1-0 at the break.
And Ronny Deila's side found their range in the second-half - after Aberdeen had had a penalty claim turned down - as Leigh Griffiths netted from the spot before Gary Mackay-Steven and Stefan Johansen profited late on as the tiring Dons unravelled.
McInnes said: "We set out to try to go and make things happen, and I thought we caused Celtic a lot of problems.
"The first goal is always pivotal in these games and it was self-inflicted.
"They've scored from their first corner and that's three goals they've scored against us from corners, so we've got to learn.
"While there's still a lot to be pleased about, and a lot of positives to be taken from the first half, we shouldn't go in 1-0 down.
"The response in the second half was to try to get back into the game as quickly as possible and I thought we started the second half okay, and I thought we should have had a penalty at 1-0, it hits Nir Bitton's arm.
"It shows there's still a lot to learn for us, the concentration side, the set plays, the mentality at 2-0 to keep doing the right things.
"I just thought we unravelled at that stage. Once we went two down Celtic really put us to the sword."
Source: Sky Sports
