The Red Devils dominated at Old Trafford, with Burnley goalkeeper Tom Heaton pulling off 11 saves to keep Zlatan Ibrahimovic and company at bay.
The stalemate extended United's winless run in the league to four matches and leaves the club eight points behind leaders Manchester City after 10 fixtures.
Speaking to Sky Sports, Neville said it was harsh to criticise the United players on a day they did everything but put the ball in the back of the net.
"It was bizarre," the former England defender said. "I think you have to give Burnley some credit for the blocks and for the fact they put their bodies on the line.
"Plus, Tom Heaton made some fantastic saves, but I don't think I've seen United have as many chances as they had here for a long time. They should have won that game.
"It could have been six, seven or eight and Burnley wouldn't have had any complaints. They were brilliant chances."
United boss Jose Mourinho was sent to the stands at half-time after protesting against referee Mark Clattenburg's decision to not award his team a penalty for a foul on Matteo Darmian in the first half.
The hosts suffered a further blow in the second half as Ander Herrera was sent off for two bookable offences.
"United created so many chances and should have taken them," Neville added. "It's not happening for them at the moment or Ibrahimovic, who is a good finisher.
"There wasn't any negative reflections on any of the United players as I think they played well today. I don't think they could have done any more apart from putting the ball in the back of the net.
"You can sometimes have days like that. I think when you're a player in the dressing room and you've had nearly 40 shots on goal and created some unbelievable moments, you can only think, 'How have we not won that game?'
"It's a little bit of bad luck they're having at the moment – it's certainly a blow. That was a game that they absolutely dominated."