Goals from Philippe Coutinho, Mohamed Salah, Dejan Lovren and Roberto Firmino sent the free-scoring Reds up to fourth place.
They are 18 points behind runaway leaders City, but Klopp is happy with his team’s current form as they chase a place in next season’s Champions League.
“Can City be caught? I don’t know. I don’t have a crystal ball. But if they struggle, like maybe nobody with their quality has struggled before, then someone should be there to use it,” Klopp said.
“I don’t see it but if I stopped working hard the moment I couldn’t be a league champion, I wouldn’t be here.
“We have so many things to play for. It’s really hard, really intense in this league, and it’ll be unbelievable the number of points you’ll need at the end of the season to get anything.
“A lot of teams are in good shape, but City are winning all their games.”
Liverpool’s win over Bournemouth, their fourth consecutive victory on the road, leaves Klopp’s side only four points adrift of third-placed Chelsea.
They now have 34 points from 18 games, largely on target to match the 76 points they reached last season to finish fourth.
– Respect for Salah –
Egypt winger Salah has been a revelation since arriving from Roma, but Klopp is reluctant to talk up individuals.
“He’s got 20 goals but what happens if he doesn’t score from now on? He didn’t score against West Brom, when we needed it more than today,” Klopp said.
“You always talk about Mo. He knows how much I respect and like him. But I don’t go home and think: ‘How good is he?’ That’s not how it works.
“He’s a very important player for us, like the others. But I’m very satisfied with how we played in this game.”
Bournemouth manager Eddie Howe, whose team are in 16th place and only one point above the relegation zone, said: “There’s not been many times since I’ve been Bournemouth manager that I’ve felt quite like this after a match. It was a disappointing watch.
“I have to say we were well off it. We looked flat in every way. Credit to Liverpool because they played well but we’re disappointed with ourselves.”