The Reds took the lead early in the second half at the Etihad Stadium as Gael Clichy’s challenge on Roberto Firmino was penalised and James Milner calmly scored from the spot.
Sergio Aguero levelled the game on 69 minutes with a close-range finish, before both teams created further chances to score, including a brilliant opportunity for Lallana.
In the end, they had to settle for a point apiece, which leaves Liverpool in fourth place in the Premier League table with nine fixtures remaining.
Klopp said on Sky Sports after the game: “We had three or four open goals in the six yard box. They had their moments too. Maybe it’s okay, but I’m not happy in this moment.
“Give me a few hours and then I’m happy.”
The Liverpool boss was willing to admit that Manchester City were worthy of scoring, but pointed to a spell the Reds had between the 50th and 70th minutes, during which he thinks his side should have killed the game off.
“To get a point at Manchester City for each team in the world is absolutely okay.
“There were a few situations where we couldn’t defend their quality. We could have won this game, because we forced the goalkeeper into a few outstanding saves.
“We had a phase between 50-70 where we had them and didn’t close the game. We let them recover on the pitch, so they came back.
“They deserved the goal, but we could have scored more. Two highly motivated sides, both wanted to win until the last seconds”, he added.
Ih his post-match press conference Klopp was asked about a top four finish and that Merseyside derby that comes after the international break.
The next game is against Everton, they have come from behind [in the table] and it is quite impressive, so it is not only a derby, it’s another very important game.
Now we will send the boys all over the world to their national teams, hopefully they come back healthy and then we will go again. The problem is, if you do something like this [draw at City] usually it is really positive, but in our case it is not only because it means we could have done better in the other games.
In a few of them, yes, but not in all of them because of different reasons. There is one outstanding side this year – an outstanding and consistent side – and they will be champions probably. That is then well deserved and all the rest fight with all they have for the Champions League.
We are one of these sides and that’s good. If you do it, it’s a success and if we don’t do it, we will be disappointed, but we would not stop working and would not stop believing in this project. We are really convinced about the circumstances we have and we want to use it.