Mauro Camoranesi came off the bench to net an equaliser for Juve after Julio Cruz had put Inter ahead just before halftime.
"We didn't want to get a draw here, but unfortunately if you don't go 2-0 up then that is what can happen. The draw is not the right result, we deserved all three points," said Mancini.
"We were in good shape and could not have done any more to win this game - other than score a second goal!
"We wasted a great deal and in football if you do that, you get punished. I am only sorry that we were unable to seal the win, as we were deserving of that victory.
"Precisely because it was an important game we should have been more clinical and score as many goals as possible, as with Juve you can never get distracted for a second. This will serve as a lesson in future."
Mancini admitted: "This was a great opportunity to stretch out at the top, but we cannot have regrets considering our excellent performance."
"These are normal things that happen between a defender and a striker on the field, I don't think it's anything that needs to be commented on," assured Mancio.