bring down the curtain on Ferguson's final home match after more than 26 years in charge of United, than the veteran manager revealed England international Rooney had submitted a transfer request.
Ferguson, who retires at the end of the season, dropped Rooney for the Swansea match and said the forward had not been in the right frame of mind to play.
"I don't think Wayne was keen to play because he's asked for a transfer and he wants to think it through in his mind. I think that's a good idea," Ferguson told Sky Sports.
"We're not going to let him go. I think maybe he's a little bit frustrated that he's been taken off once or twice in the last few weeks."
Although Rooney was not included in United's match-day squad, he took part in the post-match victory celebrations after the squad were presented with the Premier League trophy and was also seen to share a brief on-pitch embrace with Ferguson.
Rooney last asked to leave United in 2010, when he accused the club of failing to match his ambitions, only to change his mind and sign a new five-year contract.
Speculation about his future was sparked after he was left out of the United starting XI for the crucial Champions League last 16 home game against Real Madrid in March, with England team-mate Danny Welbeck playing in his place.
He has also been obliged to play in an unfamiliar midfield role in recent weeks, due to top scorer Robin van Persie's status as the club's number-one striker.
Rumours that Rooney had asked to leave the club again first emerged shortly after Ferguson announced on Wednesday that he was leaving Old Trafford after a record-breaking 26-and-a-half-year spell in which he won 38 trophies.
Moyes handed Rooney his professional debut at the age of 16 when he was at Everton.
Rooney joined United in a £27 million ($42 million, 31.9 million euros) transfer two years later and although Moyes sued him over remarks that appeared in the player's autobiography in 2006, the pair later reconciled.
Ferguson, perhaps conscious of the Rooney problem that will confront both Moyes and new United chief executive Ed Woodward, who will replace the well-regarded long-serving David Gill at the end of the season, thanked supporters and urged them to back this successor.
"You've been the most fantastic experience of my life," he said, as fans in the crowd of 75,572 fell silent to listen to the man who revived United following his arrival from Aberdeen in November 1986.
"My retirement doesn't mean the end of my life with the club. I'll be able to enjoy watching them, rather than suffer with them.
"I'd also like to remind you that when we had bad times here, the club stood by me, all the staff stood by me, and the players stood by me. Your job now is to stand by our new manager."
Ferguson, 71, later hoisted the Premier League trophy in front of his jubilant players, three weeks after United secured an unprecedented 20th English league title with a 3-0 home win over Aston Villa.
Everton manager Moyes will take over as manager on July 1, having signed a six-year contract, with Ferguson taking up a role as a director and ambassador.
In another sign of the changing times at Old Trafford, Paul Scholes made his farewell appearance after announcing that he is to retire for the second time.
The final game of Ferguson's United reign will be at West Bromwich Albion next weekend.
Moyes was given a warm send-off by Everton's fans after his side beat West Ham United 2-0 at Goodison Park in his final home game of his 11-year reign.
"There's always a worry when you're joining another club, but Everton fans were magnificent for me today," Moyes told BBC Sport.
While Ferguson and Moyes have some measure of control over their immediate futures, the same cannot be said of Manchester City manager Roberto Mancini.
A year on from leading City to the Premier League title, Mancini was the subject of widespread reports he was about to be sacked after the side's shock 1-0 FA Cup defeat by underdogs Wigan on Saturday.
Reports in Spain suggested that Malaga boss Manuel Pellegrini has already been lined-up to take over at City.
Mancini did his case little good when he criticised City's Abu Dhabi owners for not quelling the uncertainty over his future.
"I don't know why the club didn't stop this, because I didn't think it was correct. I don't think that it's true," he said.