Jurgen Klopp's men dominated proceedings at Anfield but were left frustrated by United's defensive doggedness, as the much-hyped fixture ended goalless for the second season in a row.
Neville said United showed more ambition in the first half than they did in this fixture last season, but admitted that the second-half performance was not good enough for a team with title aspirations.
"In the first half I thought that United, to be fair, were definitely different to a year ago, there was more intent," the former right-back told Sky Sports.
"The second half drifted back towards a year ago, I have to say, where Liverpool were the only team pressing.
"United's intent and quality in the second half were nowhere near good enough. They started to resign themselves to a draw.
"[Anthony] Martial, [Marcus] Rashford, [Romelu] Lukaku and [Henrikh] Mkhitaryan were all on the pitch at various points. I expected more confidence and authority from them on the counter-attack."
Liverpool enjoyed 62% of the ball had 19 shots on goal to United's six, with Joel Matip spurning the hosts' best chance of the game as his close-range effort was brilliantly saved by David de Gea in the first half.
Emre Can wasted the Reds' best chance after the break as he blazed over the crossbar after being picked out by Joe Gomez.
Neville feels Liverpool, who have won only one of their last eight games, could have shown more ambition to force the win.
"Liverpool put in a good performance but Jurgen Klopp could have turned it up in the second half if he had wanted to," he said.
"He dared not lose. They were trying to attack and be positive but they were still measured in their positivity.
"They didn't want to leave the counter-attack open. They were making sure United didn't cut through them."