Manchester United landed an early-season blow on their ambitious rivals as they snatched a last-gasp victory in a Wembley thriller on Sunday.
Yet Kompany, whose mistake led to Nani's injury-time winner, is not concerned about the outcome and expects the FA Cup winners to provide their rivals a stern challenge this term.
When asked if the result gave United a psychological edge, the Belgium international said on Monday: "No, nothing.
"I'm sure if we would have won United would have said the same. We are very confident.
"We have seen here that even when we do not play our best game we can still be very dangerous. It was really close regardless.
"We have got a lot of potential and much to improve. Come the league, the Champions League and the FA Cup we will be ready. We are a strong team, an organised team.
"We might not have been it today, but we are going to be for the future."
City are expected to build on last season's success to make a strong push for the Premier League title.
They begin their campaign against promoted Swansea at the Etihad Stadium next Monday.
Kompany added: "It would have been nice to win it but the fact we didn't isn't going to change anything for how we have worked towards the Swansea game.
"It is good we have another important 90 minutes in the legs.
"It wasn't our best performance but when we start next Monday, that is going to be the big one. We are going to be ready."
City took command of the game against United with goals late in the first half from Joleon Lescott and Edin Dzeko.
United responded through Chris Smalling before Nani completed a fine team move to level with a superb equaliser.
With no extra time to be played, a penalty shoot-out loomed until Nani dispossessed Kompany near the halfway line in the fourth minute of injury time and raced clear to score.
It was a rare error from the normally reliable Kompany, who captained the team and is expected to be handed the role full time in place of Carlos Tevez.
"It happens," said Kompany. "You play centre-half, that is a lot of responsibility.
"Sometimes it goes your way and sometimes it doesn't. It's part of what football is about.
"I'll move on now to the next game. That's what I've always done."
The season ahead promises to be an exciting one for City with the club competing in the Champions League for the first time after finishing third last term.
Kompany said: "Every competition we start this season will be a priority for us.
"We are excited because it's a big season ahead we have been working hard.
"Come Monday it will be a big kick-off for us.
"But now is not the time to give big talk. We have to be ready for the Swansea game."
Source: Team Talk
Source: Team Talk