The France international has endured a slow start to the Premier League season like most of his Manchester United team-mates.
Pogba created two assists in a 4-0 victory over bitter rivals Chelsea FC in their season opener.
The 26-year-old missed a second-half penalty in a 1-1 draw with Wolverhampton Wanderers in their second fixture.
Neville was heavily critical of the French midfielder for taking the penalty, especially given that Marcus Rashford had netted from the spot a week earlier.
Manchester United lost 2-1 to Crystal Palace at Old Trafford before a 1-1 draw with Southampton at St Mary’s last weekend ahead of the international break.
Former Manchester United defender Neville believes that Pogba need to carry the Manchester United team given his obvious talent.
“I speak to people, apparently he’s a great lad, he trains well, he’s a really good person – to be fair, I was at the club with him when he was a young lad,” Neville told Off The Ball.
“So when people criticise him or put the pressure on him or apply the pressure to him, it’s because he’s the best, he’s the shining light.
“He’s the Bryan Robson of the 80’s now. United were in trouble, people hung everything on Bryan Robson, everybody now hangs a lot on Paul Pogba. But that’s the pressure that he wants, he wants to be the best player in the world. So now go and show us you’re the best player in the world.
“Carry this team, which is young, inexperienced, hasn’t got the most know-how, needs leaders and characters on the pitch. And I said two weeks ago on television, wouldn’t it be great if he thought of himself as being the Player of the Year this year.
“What does he need to do that? Carry Manchester United into the Champions League, win the Europa League, drive them forward.
“Take it as your responsibility, you’re at this club for 12 months and you’re going to be the best player in the league and one of the best players in the world.
“That’s what I want from Paul Pogba, that’s what I want from him because I believe he’s capable of doing it. I have faith in him to do it. But then I see an incident like Wolves, and that disappoints me. So he has to take the criticism for that.”
Pogba moved to Manchester United in an £89m deal from Serie A giants Juventus in the 2016 summer transfer window.
The club-record signing has won the Europa League and the League Cup since his move to Old Trafford.
Manchester United haven’t managed to get their hands on the Premier League title nor the Champions League crown since Pogba’s return to the club.
The Red Devils will welcome Leicester City to Old Trafford in their next Premier League fixture.
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