Rooney's United future dominated the back pages last week, with numerous reports linking him with a move to mega-rich City after he announced his intention to leave Old Trafford.
However, after receiving assurances that the club were prepared to invest in players of sufficient quality to sustain a long-term challenge for top honours, the England striker changed his mind and signed a new five-year deal with United on Friday.
Neville, who made his 600th appearance for United in their 2-1 win at Stoke on Sunday, is pleased that the issue can now be "put to bed" but could not resist a dig at the Red Devils' near-neighbours and bitter rivals.
In his column for the Sunday Times of Malta, Neville wrote: "When our top players sign long-term contracts, it obviously gives us a boost. Wayne is staying and now we look forward to winning trophies with him in our team.
"The main thing is that, after a difficult week, the best outcome was reached for all parties."
Rooney is currently recuperating from an ankle injury with his family in Dubai but could yet be fit for the Manchester derby on November 10.
Neville is confident that the player will quickly be forgiven for questioning the club's ambition, and added: "He has apologised to the fans and everyone else connected with the club so we have to put it to bed now. While there will always be fallout from an incident like this, as soon as we get back to playing football and Wayne gets back on the pitch it will all be forgotten about.
"The fans have obviously been watching it very closely. While the statement attributed to Wayne last Wednesday didn't go down very well, we all make mistakes in our lives and we've all done things we regret. United fans will accept that.
"He has always given 100 per cent when he has pulled on a United shirt, and that is the overriding factor. No-one can doubt that he loves playing football for this club and I have no doubt the fans will support him through the rest of his career here."