The 1-0 victory over City, courtesy of Georginio Wijnaldum's eighth-minute header, restored the second-placed Reds' six-point gap to Antonio Conte's side, skysports.com reported.
Chelsea extended its remarkable winning run to 13 games with victory over Stoke but — much to Klopp's delight — it has not been able to extend any significant advantage.
"They won 13 games in a row. Not bad. Can you imagine how annoying it is when you win 13 games in a row and there is still one team only six points behind?" the German said.
"It is unbelievably difficult in this league but we cannot have a look at Chelsea, they are unbelievably strong and they are on an outstanding run.
"We have to win our games and see where that takes us."
Asked whether Liverpool could replicate a run similar to Chelsea, Klopp, whose side has won four in succession, added, "You need to win 14! Nobody really thinks we can do it.
"It will be difficult enough to win at Sunderland. I know what we have to do to win the next game but not to get Chelsea.
"I'm pretty sure I said in the first few meetings that we want to be the most ugly-to-play side in the league.
"The boys made a big, big improvement and wonderful development. Now we are really good in possession and these things so we didn't have to defend like we defended last year nearly each week so often, but we still can mix it up and that's what we need."
Klopp played down the significance of victory over Pep Guardiola's side, despite it giving them a four-point cushion over their top-four rival.
"I don't know if I need to be anything but to be happy when we win against City. Actually I know I don't," he added.
"We got the three points. I really thought we deserved it and that is the only thing which is really important.
"We are in the region of the table where we need to be."