City were drawn in Group D alongside Real Madrid, Borussia Dortmund and Ajax in a group that pits four national champions against each other.
Kompany admits that the draw has been tougher than last season's, which saw Roberto Mancini's side line up against Napoli, Bayern Munich and Villarreal.
"I thought it couldn't get more difficult than last year but there you go," said Kompany.
"It's a great challenge. I think we are the sort of team which gets better as the challenges get even greater. Games like this are why you are in the Champions League.
"There won't be any moments where we will be surprised. The motivation will be sky-high, the atmosphere great. I couldn't think of a better way to play the Champions League."
Kompany captained the Manchester City side that won the Premier League last season.