The Belgium defender said: "It was a good performance, but we learned a lot. We only saw Robinho and Zabaleta for the first time on Friday, so there a lot of things that will be better in the future when we all play together more and learn more.
"We saw some moments of the kind of football that the fans like to see, and we showed that we can be dangerous at any time. If you don't concede the first goal you have to stay ahead for the rest of the game, but Chelsea are a great side and sometimes you just have to accept that your opponents are that bit better.
"It will always be difficult against a top-four team, but I am sure we will improve during the season. We have shown some good things already and I am looking forward to what is going to happen here. It will be interesting when we play those sorts of teams later because this is a team of the future."
On Robinho and Pablo Zabaleta, Kompany also told City's website: "They are both great players who will improve the level of the squad. Everybody knows that there is a lot of quality in City's squad now, but we need time to play together.
"This is clearly a team for the future, there are a lot of young guys here of a good standard, but against a team like Chelsea with a tradition of winning a game no matter what happens it makes for a difficult situation. I'm sure when we start training with each other more then eventually there will be more nice moments for the crowd."