The Dons shipped three goals in a frantic opening 11 minutes before Jonny Hayes pulled one back.
"But for that 10 minutes, we could have won the game," McInnes said.
"As bizarre as it sounds - you can't give Celtic a three-goal head start and expect to get anything - we had chance after chance, so we actually could have."
Hayes' sumptuous strike came after Dedryck Boyata, Stuart Armstrong and Leigh Griffiths earned the visitors a quick-fire lead.
Aberdeen were also denied a penalty when Celtic goalkeeper Craig Gordon felled Graeme Shinnie in the away box.
"We should get a penalty - big decision, it needs a big referee to make that decision and we didn't have that tonight," McInnes told BBC Scotland.
"For me, it was a stonewall penalty and we had plenty of the game left to really go and rattle them further."
Aberdeen have now lost all four league encounters with the Scottish Premiership champions this season and were comfortably beaten by Celtic in November's League Cup final.
McInnes' men will have one last opportunity to topple the Glasgow side in the Scottish Cup final on 27 May.
"I think we've been gradually getting closer to them in terms of getting a result," the Dons boss added.
"There are acceptable ways of losing and tonight was one of them, because we did recover and the players deserve credit for that.
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"But we do need to learn from the start - it might be the difference between getting a winners' medal in our pocket or not.
"I feel that game will make us more confident going into the final, even though we've lost.
"It needed to be a performance where they knew we were there, they felt us, they knew we were making contact, they knew we weren't going to get pushed aside and we took them on."
Derek McInnes says his Aberdeen side had enough chances to finish on the right side of their 3-1 loss to Celtic.