Their win at Stamford Bridge was far from pretty and they were hanging on at the end after N’Golo Kante’s fine goal got Chelsea back in it.
Klopp, who watched City’s highlights after training on Saturday, says it is points that matter and that is where Liverpool have the early advantage.
Asked what he thought of City’s win, the German replied: “I wanted to see the goals. I saw a 2:50 summary when we left the training pitch. I saw eight goals and three times the woodwork.
“I have to watch fully to really understand it. If it can happen against anyone it can happen against City. It happened to us a few years ago when we lost 5-0.
“I said it before, they are the best team in the world. I don’t want to put pressure on Pep [Guardiola], they are brilliant in moments—we are not bad as well.
“This type of football not a lot of teams can play, but we play in our way, we try to win football games. In the end we need to get the points, there is no competition in technical things, it is about the points.
“I still don’t see that it is only two teams. At the moment we don’t have to think about it. It’s matchday six, we are talking about the title with 32 games to go, I think that it is a bit early.”
It looked like being a routine three-point haul for the Reds as Alexander-Arnold’s brilliant free-kick was added to by Firmino’s free header.
Chelsea, who had a goal ruled out by VAR at 1-0, did not wilt after the break, though, and Kante’s fine individual strike had Liverpool hanging on.
“It was very good in moments, Chelsea had their moments of course because they are so good,” Klopp said.
“We scored two wonderful goals, we had a lot of brilliant pressing situations but we didn’t use the ball well enough.
“After half-time we had two big chances and it could have been three or four but we didn’t score.
“When Kante scored his great goal it was game on. It’s a difficult place to come, it’s a while ago that we won here. It’s a big win.
“The boys did really well, they fought really hard. I don’t think there is any other way to win here. It’s a big win.”
Frank Lampard is still waiting for a first home win in charge of Chelsea and admits he is concerned by their inability to win at Stamford Bridge.
But he was also enthused by their second-half performance.
“It’s definitely a concern, we want to win at home,” he said. “Against Liverpool you know you can lose, they are a strong team and it can happen. I expect the home win to come soon.
“It is hard to accept congratulations after a loss, but the way we played in the second half is towards where we want to be.
“Energy, passion, moving the ball quickly, changing the play, getting crosses into the box, things we work on and we did it against Liverpool.
“I don’t mind losing, I will take today but it now needs to translate to points because that performance week in, week out is going to amass points and we need to do that and keep improving.”