The 28-year-old Argentina striker held up a banner designed to look like a gravestone and bearing the words 'RIP Fergie' as City celebrated their title triumph over Manchester United during an open-top bus parade.
Manchester City later released a statement apologising to Ferguson and criticised Tevez while the player - who it is believed took the banner from a fan - also said he "didn`t mean any disrespect".
"The creation of the tasteless material is in itself reprehensible and in accepting and brandishing it, Carlos has made a significant error of judgement," said a City spokeswoman.
"The club wishes to express its sincerest apologies to Sir Alex Ferguson and Manchester United Football Club for any offence or distress caused."
Tevez for his part said he had just got carried away.
"I got carried away in the excitement of the moment and I certainly didn't mean any disrespect to Sir Alex Ferguson, who I admire as a man and a manager," he said.
There was speculation it could have been a reference to a comment made by Ferguson in 2009 when he was asked whether United would ever be underdogs to their city rivals.
"Not in my lifetime," the United manager said.
Tevez left United in 2009 and joined City.
He spent several months in exile earlier this season after refusing to come off the bench during a Champions League game at Bayern Munich in September but returned to play a key role in the title run-in after making peace with coach Roberto Mancini.
City were crowned champions for the first time in 44 years on Sunday when two injury time goals saw them to a 3-2 win over QPR that consigned United -- 1-0 winners at Sunderland -- to second place on goal difference.