Despite securing a convincing win away to City on Saturday, Klopp believes his side need to improve their mentality to ensure this becomes a regular occurrence.
Speaking to NBC at the Etihad Stadium after the game, Klopp spoke of the surprise in the dressing room at half-time, with his side 3-1 up after goals from Philippe Coutinho and Roberto Firmino, as well as an own goal from Eliaquim Mangala.
The 48-year-old identified this as an area to improve as his side move forward from this win.
“I’m really, really satisfied with the performance. It was far away from perfect but it was in many moments really good,” he said.
“We had to disturb their buildup play – because if you let them play how they want, no chance.
“We didn’t defend perfectly, we didn’t move enough on the wing, we had it too much in the centre, didn’t move enough on the ball side.
“But when we got the ball, our counter-attack was not too bad tonight!”
Liverpool overran Manuel Pellegrini’s side throughout the evening, with a confidence in their attacking play exposing flaws in the Chilean’s team selection.
But while the likes of Firmino and Coutinho showed their belief on the pitch, Klopp feels this must translate to other situations.
“There’s a long way we have to go, it’s not easy because we have no time really, and when we have time all the players are around the world.
“We are far away from finished, but the character of the team is really good.
“When you watch Liverpool you see they are ready for work, but of course we have to work on their mentality.
“Today I said to my players at half-time, ‘it looks a little bit like you’re surprised that you have a 3-1 lead!’
“So we have to learn to win, to be in the lead. It’s far away from perfect, but it’s a big step.”
Liverpool have now secured two big victories during Klopp’s reign, with this win joining the 3-1 defeat of Chelsea earlier in November.
The Reds’ big-game mentality is swiftly developing under Klopp, but the German clearly feels there is a way to go before his side can be considered genuine challengers.