It is the first time in history an English team has won the men’s domestic treble – the Carabao Cup, Premier League and FA Cup.
City have now lifted five of the past six domestic trophies available.
“What a club, what a privilege,” Kompany told BBC Sport.
“It started with the manager, he sets the standard at the start of the season and said we had to go back-to-back [Premier League title].
“It’s the best team in the world for me. To set such a high standard for so long – not just for one year but two years running now.”