The Barclays Premier League champions have made an indifferent start in the competition having collected just one point from their opening games against Real Madrid and Borussia Dortmund. To retain hope of progressing from Group D, City must now make the most of back-to-back encounters against Dutch champions Ajax, starting on Wednesday night in the Amsterdam ArenA.
Kompany said: "We look at the competition thinking we have a big chance and are capable of winning every game. We go into the game with a very good positive attitude and we feel we have had a good start to the season."
He went on: "We want to win all the remaining games. All of the games will be very important but I don't think we are looking at any and thinking we can't win.
"We will always have a feeling we can go into a game to win it."
Despite making an unbeaten start to their Barclays Premier League defence and sitting in a healthy third spot after eight games, City have also not yet played with last season's swagger domestically.
Much like the team, the influential Kompany has found his own form under scrutiny. The 26-year-old was at fault as Real Madrid snatched a last-gasp winner against them at the Bernabeu last month and his error preceded James Milner's sending-off in the weekend win over West Brom.
The Belgian has also been troubled by a calf injury in recent weeks but he still feels on top of his game and takes further encouragement from his team-mates.
Kompany said: "My fitness is great, I'm in top form and the international game showed it as well. I'm just looking forward to the many games that are coming.
"When it comes to character and spirit and strength to overturn situations - you can only achieve that collectively. There is no such thing as a one-man team."
Source: PA
Source: PA