City ran out 2-1 winners at Old Trafford thanks to goals from David Silva and Nicolas Otamendi as they moved 11 points clear at the top of the Premier League.
Speaking on 'Super Sunday' following the game, Neville waxed lyrical over Pep Guardiola's side, describing them as 'on a different level'.
"I thought City were a different level to United," Neville explained.
"I thought in the first half United looked anxious when they were on the ball when they won it back. In the second half United didn't have the quality.
"It's tough to do what City have done today; to go to Chelsea and play like they did and come here and play like they have, showing authority and confidence.
"The goals were scruffy and Jose won't believe they've conceded two goals from set pieces, but not many teams have come here in the last 25 or 30 years and dominated like that.
"You are talking about Barcelona or Real Madrid. Not many teams come here and do that. I even saw some United fans at the end clapping off the City manager and players.
"Seventy thousand United fans have walked out of there today thinking the best team have won.
"You can't have too many complaints. It could have been three or four in the end."
Meanwhile, the former England defender also hailed City midfielders David Silva and Kevin De Bruyne and questioned United boss Jose Mourinho's decision not to man-mark the pair.
"After about five minutes I thought 'this is going to be a long day," he said.
"I've watched City numerous times this season and if you let Silva and De Bruyne get on the ball and control the rhythm of the game you're in trouble.
"I thought Mourinho would have man-marked them and got in their faces. Let them go to Fabian Delph, Otamendi, Kyle Walker or even Fernandinho but those two shouldn't be getting the number of passes in the game.
"To me, when they influence the game you are having a nightmare and they influenced the game far too much.
"Have Nemanja Matic and Ander Herrera got the legs to do it? I wondered whether Jesse Lingard would go and mark Silva and if Herrera would go and man-mark De Bruyne and stop those two.
"They are so exceptional those two, they are at a different level. Follow them and stop them."