Rooney's relationship with Ferguson, which was widely reported to have broken down as a result of those allegations, appeared to worsen when the player publicly contradicted claims by his manager that he had been struggling with an ankle injury this season.
The 24-year-old Rooney said it is primarily Ferguson who has convinced him to remain at the 18-time English champions and is now determined to get back in United supporters' favour.
"I'm sure the fans over the last week have felt let down by what they've read and seen. But my position was from concern over the future," Rooney said. "The fans have been brilliant with me since I arrived and it's up to me through my performances to win them over again."
Rooney joined United in 2004 for 26.5 million pounds and helped the club to Premier League titles in 2007, '08 and '09.
He also was a member of the side that won the Champions League in 2008.
"I'm sure everyone involved with the club will now get behind Wayne and show him the support he needs to produce the performances we know he is capable of," Ferguson said.
Rooney is currently out with an ankle injury sustained in training on Tuesday, on the eve of United's Champions League match against Bursaspor.
He has scored just one goal for his club this season - a penalty against West Ham - having netted 34 in all competitions last term to help earn him the Premier League's Footballer of the Year award.
Nothing's shocked me more: Lou Macari
The former Manchester United midfielder Lou Macari feels Rooney will have to work hard to rebuild relationships with his team-mates after deciding to remain at Old Trafford.
The England striker today agreed a new five-year contract, having earlier in the week insisted the club no longer matched his ambitions.
"I'm shocked. Nothing's shocked me more in football than this week," Macari told Sky Sports News.
"I thought this week leading up to today was enough but I just couldn't believe it when I got the news what had happened."
Rooney on Wednesday issued a statement confirming he had refused to sign a new contract, saying he was concerned about the "future squad" and the "continued ability of the club to attract the top players in the world".
"His statement was undermining the players, was undermining the manager," said Macari. "Saying that the manager's got no ambition and the club's got no ambition and all that. You're pointing
the finger at everyone at Manchester United, not just the owners in America who probably that finger was being pointed at.
"So there's a bit of rebuilding to be done. I think supporters hold the key to how well Wayne does in the future, whether they're going to forgive him and accept him back."