Granit Xhaka and Danny Welbeck scored in a three-minute spell early in the second half as the Gunners ended the visitors' 25-match unbeaten run in the Premier League.
Mourinho made eight changes for the trip to north London with one eye on the Europa League semi-final second leg against Celta Vigo at Old Trafford on 11 May.
Neville admitted that United were not good enough to capitalise on rival teams dropping points in the race to qualify for the Champions League.
"I think making eight changes here today was a step too far," the former United captain told Sky Sports.
"They have been resilient over these last few months with obviously not losing a game in the Premier League, but then when they've had chances to capitalise on teams dropping points, they've never been able to step up and get into that top or get close.
"Ultimately, Man United have been riding both horses full pelt for the last couple of months and you've always felt it would be one game too far and I think today, it felt a little bit like that."
Neville believes that United's 1-1 draw with Swansea last weekend dealt a hammer blow to their top four hopes, but the former right-back does not think that the Arsenal defeat will have an effect on the home encounter against Celta Vigo.
"His team are short this season in terms of the Premier League and they have to focus everything on Thursday. I think they will be okay because of the fact it is a completely different competition," Neville said.
"My view is that before this game, Jose Mourinho's language in his press conference made it feel like it was all around the Europa League with two games in the competition compared to four in the Premier League."