Sky Sports pundit and former United defender Neville, who has repeatedly insisted that Rooney would be going nowhere, says the forward was impressive throughout the game and showed why David Moyes can’t afford to let him go.
He told Monday Night Football: "A couple of weeks ago I said there was no way Manchester United would sell Wayne Rooney to Chelsea. It would improve them immensely and it would weaken Manchester United.
"He’s a player that’s important to them and we saw tonight the fans gave him a great reception. We saw from Wayne Rooney one hell of a performance for his first 90 minutes of the season.
"It was the way he put the effort in tonight. There was once when he ran back to the touchline with Ramires and had the whole crowd up on their feet.
"He didn’t give the magic moment, the goal that would have crowned it off. There was a point in the first half when he could have passed to Robin van Persie that would have been ideal. Maybe in a couple of weeks he’ll get a little bit sharper and a little bit more game-wise.
"But for a first 90 minutes after being out for such a long time, in a big game under big pressure and with everybody looking at him, that was a pretty good night for him and I think Manchester United will keep him."
Mourinho had previosuly indicated that he would launch another bid for the striker after the game, but Neville says United boss Moyes would lose credibility if he allows him to leave.
And he said it’s good for football that both Rooney and Luis Saurez have been denied the moves they craved this summer.
Neville added: "I don’t know what’s going to happen with Suarez at Liverpool and we don’t know what’s going to happen to Rooney in the next week.
"But clubs like Liverpool and Manchester United have got to be strong. If they don’t stand strong then we’re done, finished and we might as well all pack in.
"They have got two and three years left on their contracts, they are brilliant players and they are fantastically important players for their football clubs. Are those clubs are going to be bullied into selling players?
"Mourinho said Manchester United is a special club and the fans will still come around Rooney – and I’m sure Suarez will get a great reception if he comes out at Liverpool in a few weeks’ time.
"That has got to be a result for football because if these two clubs don’t stand up to it then who will stand up to it?
"Wayne Rooney hasn’t handed in a transfer request, he hasn’t refused to play and in fact tonight has done everything but that. He’s actually put in an incredible shift. All you can be is professional and the fact of the matter is that he respects the club’s wishes.
"People come and try and pick up your players all the time, so you’ve got to stand there and be strong. When you say that you’re not going to sell, you’ve got to mean that you’re not going to sell or else you lose all your credibility and substance. That’s what Manchester United are all about.
"I don’t think they’re going to sell Wayne Rooney in this next week because it will make them look weak – and they’re not weak."