City have been drawn alongside Real Madrid, Ajax and Borussia Dortmund, the champions of Spain, the Netherlands and Germany respectively, in the group stages of the Champions League.
Roberto Mancini's men failed to progress beyond the first round last season after coming up against Bayern Munich, Napoli and Villarreal and the task could be even harder this time.
But Kompany said: "That is why you are in the Champions League. I thought it couldn't get much more difficult than last season but here you go.
"It is a great challenge. I do think we are the kind of team that gets better as the challenges are greater. That is perfect for us. There won't be any moments where we will be surprised."
He added: "The motivation will always be sky-high. The atmosphere will be great in each of the six games we have in the group. I couldn't think of a better way to play the Champions League."