City were expected to face a stern test at Old Trafford as they tried to close the gap at the top of the table, but they swept aside their near neighbours in ruthless fashion.
Edin Dzeko netted a double, including an opener after just 42 seconds, while Yaya Toure's late strike wrapped up a convincing win, leaving City three points off leaders Chelsea with two games in hand.
But Kompany is refusing to get carried away and believes Saturday's trip to fourth-placed Arsenal is another potential stumbling block.
"It's just one little step. The other teams are still very good," said the Belgian defender.
"I mean games have to be played. As long as we don't have the points, I don't consider ourselves there yet.
"With the game against Arsenal, obviously it's good in a way, because you don't have to make a big effort to get the lads focused again."
Team-mate Samir Nasri hailed his side's impressive display on Twitter, suggesting that City are now the dominant force in Manchester.
"Great win, great team performance amazing support like always. Manchester is blue," he tweeted.