The England international signed for the Gunners on transfer deadline day for around £16m.
Neville, who now works within the England set-up, admitted that he was at a loss to explain why Welbeck was offloaded to one of United's main rivals.
He told talkSPORT: "I can't work it out [why Manchester United sold Welbeck]. After all the prices I've seen paid this summer and, obviously I've been working with him the last week, I'm thinking how is it just £16m?
"There's been right-backs and left-backs galore who have been bought for £15m this summer. How have they got him for £16m?
"I can't work it out to this day, it's a strange one. It really does feel strange that it's a centre-forward and actually it's helped out a competitor, someone who will be vying for those third and four places with United this season. I'm struggling to understand the logic behind the deal in two or three ways really."