City slumped to their first Premier League defeat of the season at the hands of Sir Alex Ferguson’s men at the Etihad, with the Belgium defender forced off after 21 minutes with an injury.
The loss left Roberto Mancini’s men trailing league leaders United by six points going into the hectic festive fixture schedule.
But Kompany, who is expected to be fit to face Newcastle this weekend, is convinced the champions can retain their crown as long as they can improve.
“In my mind, there is no difference other than we now know we can do it, so if we apply ourselves correctly we can win it again,” said Kompany.
“Of course, as champions you start most games as favourites to win and teams tend to sit back a little bit more and wait for you to take the game to them – then try to catch you on the counter-attack.
“Teams may have more respect, but they are not naïve with it and that makes each game a bit trickier than it was last season. It’s an honour to be defending the Premier League title, so you have to take everything that comes with it.
“The message was very clear for everyone at the start of the season – we can’t sit back and just expect the success of the last campaign to land in our laps again.
“We have the ambition to improve on our achievements last season and do better again. That’s our aim and what we work towards every day in training.
“We’ve learned a lot from winning the title but I still think there is a lot of room for improvement.”
MORE: The latest football news