Liverpool emphatically capitalized on Tottenham's 3-1 defeat to Wolves as it recovered from going a goal down by cantering to victory thanks to a hat-trick from Roberto Firmino, a Sadio Mane strike and a Mohamed Salah penalty, FourFourTwo reported.
And Klopp is adamant his team's current lead means little, telling a post-match media conference, "When we play against Man City it could be four. It's possible.
"I'm not the smartest person in the world, but I'm really not an idiot – not always, at least. That's really nothing. It's absolutely not important how much points you are ahead in December, even in the end of December.
"Before the game we heard because it was on all the screens about the result of Tottenham. Did you think the party started already? I didn't see a smile in any faces in the dressing room. Just see it and then go on.
"We came here in that situation with 54 points after 20 matchdays now completely being focused on the situation. Now it's not about creating headlines, creating stories. It's still about preparing football matches, play them as good as you can and try to get as many points as you can. That's it.
"In the moment it feels like [a] marathon what we are running. Before the marathon, the weather is brilliant, new trainers, new shirt, new everything. The people say, 'You will win today'. But first I have to run.
"The people all around us are buzzing and one guy has to run. We have to run. That's what we try as good as possible."
Firmino was able to complete the hat-trick as usual penalty taker Salah gave the Brazilian the ball for the second spot-kick, a gesture that amazed Klopp.
He said, "2018 ends with a Christmas present from Mo Salah. I love it, the gesture. He gives the ball to Bobby and he can score a hat-trick.
"That's just a nice thing. In the moment, I was not too happy because in training Bobby doesn't finish with penalties too often, to be honest. Obviously today it was his day and absolutely okay.
"Look, it worked so it was one of the nicest things I ever saw in my life. Really I don't know a lot of players who would do that. When I saw him then celebrating with Bobby that was then like 'wow'. Just outstanding. So far, the gesture of the season – really, really nice."