The Gunners moved two points above the Red Devils and into fourth place with a 2-0 win at the Emirates on Sunday, courtesy of an early Granit Xhaka strike and a Pierre-Emerick Aubameyang penalty.
However, Neville wasn’t concerned by the performance of his former team and believes that the game was decided by small margins.
"I think Ole will look towards how they lost, but I think I've said it before, that is an acceptable way to lose 2-0,” he told the Gary Neville podcast.
“You can never say at Manchester United that it is acceptable to lose 2-0, but today was. There were four strikers on the pitch at the end of the game, they had as many chances as Arsenal, more possession, but Arsenal, on the day, had more of an edge.
"There was something wrong with United - cobwebs, out of their legs, mentality - something wasn't right and in the end, I think that's what cost United. Sometimes when you're not right physically, you don't get that little bit of luck to go with it."
It was Solskjaer’s first defeat in 13 league games since he took over from Jose Mourinho on a caretaker basis in December.
The Norwegian has also led United to the Champions League quarter-finals and Neville believes he should be rewarded with the manager’s job on a full-time basis.
"United have it all to play for,” he said. “I do think Solskjaer will get the job because after what he has done in these three months, he deserves a shot at it.
"The board at United have tried everything - they've tried one of the best managers in the world in Jose Mourinho, the experienced guy in Louis van Gaal, who had been at all the biggest clubs in Europe and then you think about giving it to David Moyes, which is the approach the club had always taken about the British manager who deserves a chance.
"The only thing they've not done is given it to one of their own who understands the club. Solskjaer has connected the club, the results have been incredible and there was always going to be a defeat.
“But it's not been a defeat that's embarrassing, Manchester United could easily have drawn or won that match, it's just gone against them in the big moments.
"I think ultimately, what Solskjaer has done already when they drew with Burnley or lost in the Champions League to PSG, is got them to respond straight away.
"One defeat is a blip. Two defeats, people start to ask questions. Three defeats is a bit of a crisis and four defeats, you're in trouble - that's the way it works in modern football.
"But he has built up too much favour, he's done too much in the last three months not to have a shot at this."
