Klopp’s side answered City’s avalanche of goals against the Hornets as Trent Alexander-Arnold’s blistering free-kick and Roberto Firmino’s header put them two goals ahead at half time at Stamford Bridge.
And despite N’Golo Kante’s great second half goal, Chelsea could not salvage a point in west London.
The Liverpool manager, whose side became the first to win their opening six games for a second successive season, said: “I watched it. I wanted to see the goals. I saw a two-minute 50 seconds summary after I left the training pitch.
“Eight goals and they hit the crossbar twice. I needed to watch it fully to really understand it.
“For Watford it was a tough day. If it can happen against any team in the world it will be City.
“We had a similar situation when we lost there 5-0 two years ago. If you have ten men the worst place in the world is Manchester City.
“I slept pretty well.”
But he added: “We knew the job we faced that before that game. I have said it before, I really think they are the best team in the world.
“I don’t want to put pressure on Pep but they are brilliant in moments. We are not bad as well, so that’s how it is.
“That’s not important. We play our football and we try to win games and if the other team is better, then we try to be at least uncomfortable for them and in the end you need to get the points and that’s what we try.
“I still don’t see that in the end it is only two teams. But at the moment we don’t have to think about it.
“It’s match-day six. We talk about the championship with 32 games to go. That’s a bit early.”
Klopp was delighted with the performance of his charges as they restored their five-point advantage to City in the table.
He insisted: “We were very good in a lot of moments. Chelsea had their moments of course. We scored two wonderful goals.
“There were a lot of brilliant pressing situations where we won the ball in the perfect space but then we didn’t use that situation well enough and we could have had many more situations.
“After half time, it could have been three or four but we didn’t score so the game was still open. It is a while since anyone won here.
“We expect to fight for everything these days. So we have a big job to do in a really difficult league.
“Everybody thinks we should be first or second, but we have to play the football for it.”