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."
Goals from Xherdan Shaqiri and Rodrigo Palacio in the opening 13 minutes had Inter in control before Stuart Armstrong pulled Celtic back into the contest.
A Hugo Campagnaro own goal less than 60 seconds later had Celtic level before Palacio struck just prior to half-time following an error from Celtic shot-stopper Craig Gordon.
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."
Mancini defended his decision to start Croatia international Mateo Kovacic on the bench, saying the enormity of the occasion was behind the move.
"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."
