City didn't win a single trophy last season, losing their Premier League crown to bitter rivals Manchester United and falling to a surprise defeat at the hands of Wigan Athletic in the FA Cup final.
Kompany believes that a repeat performance this season would see them fall short of their goals, but admits that they face a lot of competition for trophies.
"We're at a big club, so the only goal we can have is to win trophies," the Belgian centre-back told reporters.
"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."
City will begin their Premier League campaign with a home match against Newcastle United on August 17.