The Serie A outfit gave up a 2-0 lead before going 3-2 up, only for John Guidetti to score with a 93rd-minute equaliser for Celtic.
Mancini rued Inter allowing Celtic back into the contest, and said it was an area of their game they needed to work on.
"If you sit deep against teams like this then sooner or later you're going to concede. We should have tried to hold a higher line. We were tired, though," he told a media conference.
"We got off to a great start in the first half but then we thought the match was over.
"We started playing around and that was our mistake because we let them back into it. That's something we need to improve."
Just as Inter looked set for victory, Guidetti finished well – but Mancini believes it was far from a bad result for his team.
"There's always going to be regret after the way things went tonight but I don't think 3-3 in Glasgow is a bad result," he said.
"We came here looking to take the game to them and it wasn't easy. We made the mistake of taking our foot off the pedal when we were in front."
"A midfielder needs experience and he's not ready yet," he said.
"But the fact he was left out doesn't mean I don't rate him. He'll have chances to play over the coming games because he's an important player."
