Mohamed Salah put Liverpool ahead on 13 minutes with a penalty after Kyle Walker had fouled Sadio Mane, and Gabriel Jesus levelled just after the half-hour mark on Sunday.
Kevin De Bruyne then crucially missed a penalty shortly before half-time following a controversial handball decision against Reds defender Joe Gomez, and neither side was able to find a winner.
“I think in the first half, it was a demonstration of how brilliant these two teams can be, the exhibition they can put on and the Premier League can put on,” Neville said on the Gary Neville Podcast.
“The second half showed how long we’ve got left in this season. I think both teams went in at half-time and said: ‘We’ve got to calm this down a little bit.’
“I think with City being [10th in the league], my feeling was they’d be quite desperate to beat Liverpool today, damage them, get close to them – within two points and a game in hand. I was wrong with that, because I thought City would show a lot more urgency.
“I think Pep showed the respect he has for Liverpool in the second half, in that he didn’t really break away from his shape in the counter-attack.
“In that first 25 minutes it was exhilarating, the speed of play, the tempo, the passes into the front players. It was a throwback, and a little bit of throwback to the earlier [Jurgen] Klopp days – a bit more frantic. Now it’s a lot more measured, more rounded, but it caught City out.”
Man City were also caught out by Klopp’s decision to play in-form Diogo Jota in a front four with Salah, Mane and Roberto Firmino, Neville suggested, after speculation that the Portuguese winger would be left out to accommodate Firmino.
“The idea of playing Jota was like a front four, there was no subtlety to it, they were going for it,” Neville said. “It really was a brilliant display and wonderful to watch, and it just really caught City out, and it took half an hour for City to weather that storm, get into the game and realise what’s happening here.”
Neville also tried to get to the root of City’s stuttering start to the season, noting that the injured Sergio Aguero’s absence could be one of the main factors.
“You wonder if it’s just as simple as not having Aguero? It can’t be that simple. Something’s not the same. Both sides are a little bit weaker than they were two years ago, which makes the league more interesting. We’re seeing Leicester and [Southampton] and Spurs top of the league, which we like.
“There certainly is a slight cause for concern for City. They’re less precise in their attacks, and it feels they rely more heavily on one player in Kevin De Bruyne than they did a few years ago – and if he’s not on song, they don’t really create nearly as much.
“David Silva [who left for Real Sociedad this summer] is obviously a huge miss. We knew he was a brilliant player, and almost at times the glue to keep everything together, the flow in the game. So it’s a changing team, and certainly they’re different.
“They’re not as good defensively or as precise in attack, but they’re still a brilliant team. Now we’re just seeing a little bit of a drop off from that.
“Look at the league now, it’s bizarre.”