City old boy James Milner gave Liverpool the lead from the penalty spot six minutes after half-time but Sergio Aguero equalised and both sides had golden chances to win the game.
City had the better of the play and chances after that but Liverpool could also have won, with Adam Lallana's miss from in front of goal almost inexplicable.
Klopp said of the midfielder: "He's one of the best if not the best player technically I ever worked with. If he can't (explain the miss) - I thought it was because he worked so hard before.
"After the game Adam said immediately to me 'sorry', and I thought, 'Why?' Now I know why he thought he had to say sorry but he doesn't have to because his performance was outstanding."
Lallana's miss among other factors left Klopp feeling his side could have come away with more than a point.
He added: "Everybody around me was so excited - not in the dressing room, they felt a little bit like I did - but the wonderful piece of football we did and then Adam couldn't finish.
"But of course I know Aguero could have scored once or twice, a lot of penalty situations in the game. I cannot change it. But the game is positive of course, it's how you have to play against good sides.
"It was intense, we defended well. The problem is I expect things like this from us and I cannot run around after a draw against Man City. But of course it's good if you get a point in a game like this."