Neville saw a significant change in shape during Saturday's 1-0 win over Crystal Palace, Rangnick's first game as interim manager.
"I really enjoyed the game," Neville said on Sky Sports' Monday Night Football.
"Was it flamboyant football? Were Manchester United at their absolute best in their last hour? It was a struggle at times. The first half an hour they were absolutely fantastic. The last hour they got the job done.
"I came out immediately after the game thinking what a great 30 minutes that was. That is what we want to see from Ralf Rangnick at Manchester United. That is what the Manchester United players will want to see. In the last hour they just got over the line. They tired a bit.
"But I actually sat down today and I respected the last hour more than the first 30. He had 48 hours to coach his team, 48 hours to be with his players.
"We have all spent the last six or seven weeks saying that Manchester United have been a mess defensively. They had not had a clean sheet in 16 games, conceding goals like you would not believe, getting battered at home by Liverpool and Man City, counter-attacked against Leicester, Villa, Villarreal. All the other teams had cut through them.
"What Ralf Rangnick would have wanted was order. Order in the performance. I think we got that.
"Manchester United had conceded an average of 15 shots per game this season. It was eight against Palace. Five on target conceded this season. Only two against Palace.
"A big one is that on average it looked like teams were going to score 1.6 goals per game against United. You are in big trouble if you end up conceding two goals in a game. Less than one yesterday. They were more competitive, more tackles, more duels."
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