"It's exceptional, but it's early doors in the season, and we want to put it aside a little bit and just focus on the next game," Kompany told the club's website.
"Hopefully we can continue such a special start. I think when you're pushing the boundaries like this, the main thing for yourself is to always feel like you can achieve even more, and more.
"We've got no silverware for it, and therefore so many reasons to just stay calm about it. Hopefully this is just something at the start of a beautiful story."
Pep Guardiola's team finished third in the league last season and ended the campaign trophyless and defender Kompany is wary of a repeat this time around.
"We have played well last season as well, and therefore we need to be cautious that it's not just about how well we play, but how much we can actually do the damage when we're on the pitch," Kompany said.
City top their Champions League group and face Feyenoord in their penultimate group stage match on Tuesday.
(Reporting by Aditi Prakash in Bengaluru; editing by Sudipto Ganguly)
