The Mirror says Jones posted gleeful messages on Twitter as goals against Blackburn Rovers by Antonio Valencia and Ashley Young sent Manchester United five points clear of City at the top of the Premier League.
The defender kicked off with: "Yeahhhhhhhhhhhh united united united", before following it up with: "yeahhhhhhhhhhhhhhh what a goal!!!!!"
After Monday's game, he said: "Game over! Ashley Young you king!"
But Blues fans were less than impressed, and sharp-eyed City officials gave him a dressing down.
Jones, from South Wales, has now tweeted: "I am sorry for causing offence. I shouldn't have said those things. The club has reminded me of my responsibilities."