The victory at Old Trafford also extended City's lead at the top to 11 points with 16 games having been played so far this term.
However, De Bruyne said City's focus was only trained on the next match – Wednesday's trip to Swansea.
"Lots of teams lost points this weekend so it is a big one for us [the win] just to put more pressure on the rest. We have to enjoy it and then focus again for Wednesday," said the Belgian.
"It is a big gap. If we slip up we are still in the lead. We can't be complacent. We need to do what we have all year. I prefer to be 11 points ahead than 11 points behind that's for sure."
Asked whether he was pleased with how the derby had panned out, De Bruyne replied: “If you come away with a 1-0 lead, yes – at 1-1, no.
“That’s the way it goes. There were two teams with a lot of quality. It was a nice game to watch with the intensity and the duels. A real derby.”
Team-mate Fabian Delph agreed that there was no way the City players would be taking anything for granted going forward.
But the left-back added that it was enjoyable to have secured the Mancunian bragging rights.
"It’s far too early (to talk of titles). I’ve said in the past: we’re taking each game as it comes. We’re not looking to the past or the future – just to today," said Delph.
"It’s probably the sweetest win of the lot. Derbies are always like this – hectic and end-to-end. We had a game-plan and stuck to it. The fans are happy."