"The creation of the tasteless material is in itself reprehensible and in accepting and brandishing it, Carlos has made a significant error of judgment," a City spokesman was quoted as saying.
"The club wishes to express its sincerest apologies to Sir Alex Ferguson and Manchester United Football Club for any offence or distress caused."
Tevez also apologised.
"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.
Many fans on the two-mile route were too young to recall City's last title triumph in 1967-68 when they finished two points clear of United.
Others, with their team trailing QPR 2-1 in stoppage time, had poured out of the Etihad Stadium believing Roberto Mancini's side had blown the title before late goals by Edin Dzeko and Sergio Aguero snatched it from United's grasp on goal difference.
"It was an incredible day yesterday but the support we've seen here on the streets today almost matches it," said City goalkeeper Joe Hart.
"The fans are brilliant and that they think so much of me means everything. They know this is my club and the only place I want to be."
Over the years City have been mocked by United fans and this was their chance for payback.
As the United players drowned their sorrows two miles away at the club's annual player of the year awards night at Old Trafford, City players and fans partied on the streets.
Manager Mancini wore a blue and white City scarf as he waved to supporters, many with their faces painted in the club's colours, from the steps of Manchester town hall.
"I love our supporters they are incredible and I really love days like this," Mancini said.
"I hope we have many more. I didn't sleep much at all last night because it was impossible with the emotions of what happened on Sunday. But I am very happy. I need a rest now - we all do - so we can come back fresh for the start of next season."
Graham Jackson, a 64-year-old City supporter, summed up the mood of euphoria.
"I thought I was going to my grave and never see them win it so I am so made up, I tell you," he said.
Another, Gary Aldridge, added: "I have never seen so many grown men cry, on the streets, it's just unbelievable."
There were a couple of notable absentees from the parade in City's controversial Italian forward Mario Balotelli and influential midfielder Yaya Toure.
Balotelli had flown back to Italy following his international call-up for next month's European Championship.
He also missed the FA Cup parade last season, which marked the end of City's 35-year wait for a trophy, after being granted permission to return home.
Toure, a driving force in City's title charge, was in Monaco receiving treatment for an injury suffered against QPR.
But even their absence failed to spoil the party, certainly not for the man selling inflatable European Cups who did a roaring trade.
Next year City fans will hope their team is parading the real Champions League trophy through the streets of Manchester. — Reuters