The Manchester pair boast identical records at the top of the Premier League after five matches, each picking up 13 points from a possible 15 and scoring 16 goals in the process.
Klopp's men are already five points off the pace, having dropped points in three games this season ahead of their weekend clash against Leicester City, and the German coach concedes that the level of scrutiny on the Reds has now increased.
"Everywhere [the expectation] is the same, but here it is a little bit more," he told reporters. "When the Manchester teams are flying, that makes it even more difficult but I cannot change this. What I can do is cool the situation here down and do the right things again and work on the other things. That is how it is always.
"You really think there would be one per cent of a reason I would panic? If you think I should panic, why are you talking about it? It's football. We have eight points. In four games we were the clear better side but we didn't get the results. Now we could panic because of not getting the results or we say, 'It's still not good enough playing football'.
"Do you think any team in the world loves playing against us in this moment? I'm not in panic. It sounds like we have nil points and are the worst team in the league. Yes, we obviously have problems. That's why we only have eight points and not 15, that's the situation."