United failed to take their chance to move level on points with Man City, after throwing away two leads in a thrilling second half at Old Trafford.
Goals in the opening 45 from Edinson Cavani and Bruno Fernandes looked to have put United in complete control, but the game flipped in a matter of minutes after the break.
First Abdoulaye Doucoure tapped home after De Gea pushed out a cross, before James Rodriguez equalised shortly after.
Scott McTominay put the hosts back in front, but they failed to hold on to their advantage, with Dominic Calvert-Lewin poking home with almost the last kick.
The Toffees striker was allowed the chance to score with De Gea opting to stay on his line following a late free kick.
And Sky Sports pundits Neville and Jamie Redknapp claimed the Spaniard should have been more decisive to snuff out the danger.
“David de Gea, there, at the end. He doesn’t even come in line with the ball,” Neville said.
“I think you want goalkeeper to come, as Jamie said there, and eat the striker. You just want your goalkeeper to come out there and absolutely take him out.
“Goalkeepers are so quick off their line nowadays it wasn’t a great night for the goalkeeper, it wasn’t a great night for the centre-backs either and we’ve know from the start Manchester United needed a stronger centre-back pairing.
“That hasn’t changed. No point going on about it tonight. It’s cost them.”
Redknapp added: “David De Gea as a goalkeeper has got to go out there and take everything – he’s got to be brave, assess the situation.
“Because if he comes out with some authority I’ve got no doubt at all that he’d win this, smother it.
“He doesn’t come and believe he’s going to make that challenge. He was at fault for the first goal and certainly at fault there.”
It’s now just one win in their last four for United, with Neville believing mistakes could cause his old side “serious trouble” in the coming weeks.
“If you look at the period that they’re in now they’ve definitely turned a little bit. Draw against Arsenal, Liverpool, lost against Sheffield United, drawn tonight. So the results just starting to swing a little bit the other way.
“I have thought over the past few months that the performances haven’t been fantastic and at some points the results would catch up. But actually tonight the surprise for me was that they played well.
“But if you make mistakes like that in football you’re going to be in serious trouble.”