The England international had an opportunity to give his side a lead in the final quarter of the match after Roberto Firmino set up the former Southampton man. However, the 28-year-old fluffed his shot and the incident saw the Merseyside club fail to take the lead for the second time in the match.
James Milner's penalty put Liverpool ahead in the second half, only for Sergio Aguero's goal to cancel the lead. The visitors could have walked away with three points if Lallana had found the back of the net 11 minutes from time.
"After the game Adam immediately said 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 today was outstanding again," Klopp explained, as quoted by the Liverpool Echo.
"Obviously he is one of the best, if not the best, player technical wise I've ever worked with. If he can't (score), then I thought because he had worked so hard before.
"The goalkeeper was good today, so maybe he made a movement. Or he was surprised that we played like this because we did not 20 times before. But these things can happen."
The draw has seen Liverpool sit fourth in the table with 56 points from 29 games, one point behind third place City, who have a game in hand. The Reds' arch-rivals Manchester United are fifth with 52 points and have two games in hand. A victory in those two matches will see the Red Devils move above the Anfield club in the league table.
Liverpool face Everton in the Merseyside derby at Anfield on 1 April after the international break.