Their 3-1 win at Anfield left City fourth in the table, with Leicester and Chelsea the Reds' nearest challengers eight points back, and Pep Guardiola knows his side face a tough challenge if they are retain the championship they won by a point from the Reds last season.
But he too pointed to the fact there are still 26 matches remaining - and Liverpool have a hectic December and January - which offers them some hope.
Klopp, however, is taking it one match at a time.
"Are we thinking about going through the season unbeaten? Not at all," said the German after his team made it 11 wins and a draw in the current league campaign.
"We just don't think about it. We don't feel any pressure, to be 100 per cent honest. The things that will now come up, we know about. If you are with us, then nine points is a positive. There's a long way to go.
"Other people will 100 per cent say - and have said already - that from now on Liverpool can only lose it. That's a very negative approach, but you can see it like this. But I can promise you that we don't care.
"We were completely focused on this game and not the situation in the table and how many points we are ahead of City. That's crazy. Nine points ahead of City, you cannot imagine that something like this would happen.
"But it's not important because who wants to be first in November? You want to be first in May.
"The pressure or whatever is not there yet. It will come, but at the moment it's just opportunity."
Guardiola, whose team have now lost three times this season - they were defeated only four times on the way to the title in May and just twice in their record-breaking 100-point win the year before - accepts they have a real challenge on their hands, and not just from Liverpool.
"We have three teams in front of us, maybe they have more chance to win the Premier League than us but hopefully we can sustain this mentality and try it," he said.
"In the end, if it's not enough, we will congratulate Liverpool, Leicester or Chelsea and move forward for the next season.
"Nine points is a lot, they (Liverpool) lost just one game last season. Is it their year? My colleague Jurgen can explain better than me."
City started the game with a determination to cut Liverpool's advantage to three points and dominated the opening 20 minutes only to find themselves 2-0 down - and not without controversy.
The ball deflected off Bernardo Silva's arm and hit Trent Alexander-Arnold's outstretched limb in Liverpool's penalty area, Michael Oliver waved play on and the hosts went down other end for Fabinho to score a 25-yard screamer.
A VAR check ruled the goal good and Liverpool doubled their lead when Mohamed Salah nodded home Andy Robertson's cross, with the video review ruling he was just onside.
City again felt they should have had a penalty for a push by Sadio Mane on Raheem Sterling after the break, by which time they were 3-0 down through the Senegal international's header.
Television showed Guardiola shaking Oliver's hand and saying 'Thank you so much' at the final whistle but he denied he was being patronising.
"No, it was not sarcastic. It was 'Thank you so much'. I said the same thing after the Tottenham game. 'Thank you so much.' " he added.
"Most of the time, I go over to the referees and my colleagues and I say 'good luck' all the time."
On the VAR decisions Guardiola said: "Ask Mike Riley (head of Professional Game Match Officials) and the big bosses about that. Don't ask me."