Like last year, Roberto Mancini's side have been drawn in a very difficult group - having to face Real Madrid, Borussia Dortmund and Ajax - all of whom are the current league champions in their respective country.
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Despite this, Kompany is sure that they can better last season's European results - and insists they were unlucky not to have got to the knockout stages with the points total they had amassed.
"We had 10 points last season and we should have come through [the group stages]," Kompany told Sky Sports News.
"But we have a team that is probably stronger and for us the Champions League is massive, also the Premier League - but we want to do better."
City face their first match in this season's competition against Real Madrid at the Santiago Bernabeu on September 18, before welcoming Dortmund at the Etihad on October 3.