City are celebrating their latest trophy after coming from behind to beat Sunderland 3-1 in the Capital One Cup final at Wembley.
Kompany said: "This victory means a lot to the fans; it means a lot to us.
"There is nothing better than lifting a trophy. It is an incredible feeling.
"But one thing at a time. Bear in mind for our club it is a new trophy, a new experience. I want everybody to cherish it, first of all.
"It should give us the confidence and make us believe we can still win trophies, and we need to believe for the rest of the season.
"But these experiences don't happen too many times. We will cherish every single one."
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