"When I look at it we have some important away games to come and this will be good for us - we won't be making the same mistake," he told Sky Sports.
"We lost two goals from a position I didn't thing we would.
"At this moment in time we are so disappointed.
"We have a game less (to play) and are a goal better off (than
"I thought we had the best player on the pitch in Michael Carrick," he concluded. "He was magnificent."
"We won by never giving up,"
"I felt we started nervously and Manchester United were mature and played with great belief.
"We are on the way up, we knew in the second half we could have a good go at them and take over, but unexpectedly they scored with the only chance they had in the second half and then it was a question of strength and resilience.
"I've got some lions in that team and they are getting stronger and stronger with every game.
"I felt that for a while (his side are getting stronger). We could mix up our game, we needed to be direct and we went direct sometimes in my taste a little too much.
"We mixed our game well in the second half and never gave up and in the end we have such a spirit in squad for a while now and that took over."
"The hardest thing to take is the fact we've lost the game when we were 1-0 up at Arsenal and playing well," Neville told MUTV.
"Obviously the nine-point lead would have come with it (winning) but we're not even thinking about that. We're only thinking about our own performance. The fact that we're still six points clear (of
"We've lost games before where we've had to hold our hands up and say the other team deserved to win. But I don't think this was fair. We deserved at least a draw.
"We put in a good performance for 85 minutes. We created the better chances in the first half, then we got the goal and things were going perfectly for us.
"Arsenal started playing a lot of long balls towards the end which isn't like them, so at that point we were happy.
"We defended most of that well until they got a couple of crosses in, which we didn't defend, and we conceded two goals. It was a complete kick in the teeth for us."