Following the tensed match that happened in Anfield on Sunday, a match that ended in a goalless encounter between the two reds.
However, former Manchester United defender and now sports pundits have said the Red devil must improve in some positions if they truly want to win the league.
"They have had a few years of hurt and they need to get over that.
"They need to become a club that gets used to winning again. So, winning one of the other trophies would help because it would put them on the journey.
"I also think there are a couple of things in the team. The right side has always been a problem and it's emerging as an even bigger problem.
"We have now seen this season [Daniel] James, [Juan] Mata, [Donny] Van de Beek, Pogba, [Marcus] Rashford and [Mason] Greenwood on the right-hand side.
"I actually felt sorry for Pogba on the right-hand side on Sunday. It was a toil for him. He didn't play badly, but he didn't have a good game and l didn't think he could have a good game either with [Andrew] Robertson flying that way and him not enjoying being on that side.
"If you asked him where he wanted to play in any of those front six positions, that would be the position he would like the least. It's the one that Rashford would choose least. It's the one that Van de Beek would choose least."
In the last two Premier League seasons, players starting on the right flank for Manchester United have only contributed 10 goals combined - less than half the number of the players starting on the opposite flank.
"It's a position that needs fixing," added Neville. "Not just because of the output and the goals, but because of the balance - the balance of the team is not right. It needs to be dealt with."
Manchester United's defensive record has improved in recent months - they have kept five clean sheets in their last eight games in all competitions - but Neville believes the next step is to play higher up the pitch like Liverpool did at Anfield on Sunday.
"The next point is the defence," he said. "The back four have gone from being weak 18 months ago - and l still think there is a weakness there - but they have become more solid and stopped conceding goals.
"That's not just the defence because the goalkeeper is playing better and [Scott] McTominay and Fred are doing a really good job.
"But they are having to defend really deep, particularly in big games.
"I think in top teams nowadays, and certainly the top Manchester United teams l played in, they go up the pitch that extra five yards.
"It makes your stomach churn a little bit where you think, 'There's a bit of space in behind me'.
"But this back four haven't got the personality or character to get up that extra five yards and squeeze the game. That bit will be the thing that changes the most in terms of mentality."
It might require a change of personnel as well as mentality, according to Neville.
"Ole has to take responsibility for it but he might be thinking that with [Victor] Lindelof and [Harry] Maguire, he can't get the team up the pitch a little bit more," he said.
"They have to get up the pitch a lot quicker."