City needed to come from behind against promoted Southampton to get their Barclays Premier League title defence off to a winning start in their season opener at the Etihad Stadium.
The 3-2 success may not have seen City at their most destructive but Kompany felt it was a performance full of the qualities which yielded a first league title in 44 years.
The 26-year-old told City TV: "We have always proved to be very difficult to beat at home.
"Maybe we will just get belief out of this. Maybe that is why we always keep coming back and it never seems to be finished.
"I don't even need to say it loudly. Last season proved how crucial it [team spirit] was for us, in the last games. We showed we wanted it as much.
"It doesn't matter if we have our best game or our worst game, we just keep going.
"As much as I can say we have a lot to improve on still, I can also say we can really all be happy because of great qualities of character."
City, who were unbeaten at home in the league last season, missed an early penalty but led at the break through Carlos Tevez.
Saints hit back with goals from Rickie Lambert and Steven Davis but City recovered in the final 18 minutes as Edin Dzeko and Samir Nasri struck.
Kompany said: "If everything had gone to plan we would have scored two or three goals before they even got their first.
"We missed a few chances and they used the one opportunity they had very well and the game became very difficult, but I am very happy about the reaction of the team. That is what we needed to see.
"Therefore we are very happy with the win and the result. We have to respect Southampton, they played really well. It is a good result for us."
Manager Roberto Mancini agreed his side's display was more one of character than finesse.
The Italian said: "We can't always do it like this. When we have a big chance like this, we can't take risks that might end up with us losing this game.
"We played a bad game, we were not a team. We were 10 players that tried to score.
"We showed our character but we didn't play as a team."
The one major area of concern for City was a knee injury to last season's top scorer Sergio Aguero.
The Argentinian was carried off inside the opening 10 minutes after a clash with Nathaniel Clyne.
Aguero, 24, has played down the seriousness of the problem but City are still awaiting the results of a scan to determine the full extent of the damage.
Kompany said: "Sergio is an outstanding player so if you don't have him with you then that would be a blow.
"But last season we went a huge part of the season without Carlos and we managed to cope.
"We hope we don't have to miss him but if it does happen we have enough players who can step up to the plate like Edin did by scoring a very important goal."
City return to action next weekend at Liverpool, a venue where they dropped two points last season despite a Kompany goal.
The Belgian said: "We know Liverpool's qualities. Playing at Anfield has always been a very difficult game for us.
"I would say it is one of the few games where it probably starts as an even contest.
"We will see if we can get the three points back to Manchester this time."