Pogba was sent off in the 74th minute of United's 3-1 win over Arsenal at the Emirates Stadium after he mistimed a tackle on Hector Bellerin and effectively stamped on the Spaniard.
The former Juventus midfielder will miss the top-of-the-table clash against Manchester City next weekend, along with a home game against Bournemouth and a trip to West Brom, as a result of the infraction.
Neville said Pogba would be sorely missed by United boss Jose Mourinho this weekend as he is the only player in United's midfield who can beat the opposition's high press with pace and provide service to the forwards on the counter-attack.
"You think about Pogba, he would beat [Kevin] De Bruyne and [David] Silva with the ball at his feet and break that line," Neville told Sky Sports.
"Once you break that line you're onto the weakness, you're onto those two centre-backs with [Romelu] Lukaku and [Anthony] Martial.
"City is a big game to not have Pogba. The person who can break the line is gone, but Jose Mourinho will be looking at how he can do it differently."
Former Liverpool defender Jamie Carragher urged Mourinho to adopt "old-fashioned" tactics of breaking up the game and being direct on the counter-attack.
"There's no doubt City will have the most possession, but that doesn't matter," he said. "I think United have to play the way they used to against [Thierry] Henry's Arsenal, when they were that good at keeping the ball.
"It may have to be a little old-fashioned, but to be very aggressive, using set-pieces and at times going direct and on the counter-attack, but overall, be very, very aggressive."
United are eight points behind City heading into the first Manchester derby of the season at Old Trafford.