City lost their Barclays Premier League crown last season and were surprisingly beaten by Wigan in the FA Cup final, events which preceded Roberto Mancini's departure.
Kompany said: "We're at a big club, so the only goal we can have is to win trophies.
"There's about six or seven clubs in England alone in this situation, so it will be very competitive.
"Our objective this year is to win things and to play well together. We all know that we have to be very strong as a team and bond with each other."