Kompany got on the scoresheet as City demolished the Barclays Premier League champions at the Etihad Stadium on Sunday, winning 3-0 in an emphatic display of intent.
City, who also hammered West Brom by the same scoreline last Monday, have started the campaign looking sharp and hungry and already have a five-point advantage over Chelsea
City will hope to maintain the momentum as they travel to Everton next weekend.
Kompany said: "Against West Brom we thought it was a pretty perfect performance but this was another level up
When you do it against big teams, big wins like this for us, it is what we play football for.
"The five points mean absolutely nothing but it is a blow to one of the direct contenders
They will need to shake it off over the next couple of weeks.
"For us this game only means something if we go on and produce something special again at Goodison, and it will probably be even harder again
We have a whole week to prepare for this game and that is what it will take to get a good result again."
City rocked Chelsea from the outset as they attacked with power and pace
Sergio Aguero might have struck in the opening minute but was denied then and with two more good chances by goalkeeper Asmir Begovic before finally putting City into a deserved lead after 31 minutes.
The visitors offered little until Eden Hazard tested Joe Hart in the 70th minute, although Ramires earlier had a goal ruled out after a close offside call.
Kompany made the result safe after 79 minutes when he headed home from a corner for the second game in succession and Fernandinho added a third with a powerful strike late on.
City looked a different side from the one that surrendered the title they won in 2014 in poor fashion in the second half of last season.
Kompany said: "I guess it is the advantage of having a lot of players who have had time to think a little bit on holiday and come back with more motivation than ever
At the same time, we prepared really well
You go into the season and I think we are peaking at the right time."
City also looked defensively solid with Kompany, whose formed dipped last season, shining alongside the similarly impressive Eliaquim Mangala.
Mangala's performance came as reports emerged from Spain that City could loan him to Valencia as a makeweight to land Nicolas Otamendi.
But Press Association Sport understands France international Mangala, who had a difficult first season after a £42million move from Porto, will not be leaving Eastlands.
The player himself also stated his commitment to the club after the game, tweeting: "2 games, 2 victories, 2 clean sheet! I like it ! I am a Citizen
I never give up."
Kompany also praised his partner, saying: "I thought Mangala was superb, as he was last week."
Source : PA
Source: PA