After winning the Premier League last season, City have struggled to replicate their form this year and are currently 12 points behind leaders Manchester United with seven games remaining.
However, while Kompany admits the club have made big strides in recent years, he says they must maintain their levels of performance on the pitch.
"We've made a massive progression not just on the field but off it as well," Kompany told ITV Sport.
"The club works and functions like a big club, which could not be said two years ago as it was physically impossible.
"People forget that this is a turnaround that's happened over four or five years. It's an incredible turnaround.
"In that sense I believe we've overachieved. But we've set the standard and we can't go under that now. That's the aim."Next up for Manchester City is a trip to Wembley to face Chelsea in the FA Cup semi-final and the defender is looking forward to the game.
"To play at Wembley is one of the greatest prizes of a football career," he added. "I savour it every time I play there."