Goals from Glenn Murray, Shane Duffy and Pascal Gross gave the Seagulls a comfortable first-half lead as Romelu Lukaku and Paul Pogba's efforts failed to lift Jose Mourinho's men.
Bailly was responsible for Brighton's third goal after taking down Gross in the penalty spot which the midfielder comfortably dispatched past David de Gea.
The Ivorian's challenge has been heavily criticised by Red Devils legend Neville.
"There are five centre-backs at the club. Is there a pair among them who you would trust to take you to a title? That’s the question Jose [Mourinho] needs to answer," Neville was quoted as saying by Daily Mail .
"Every single United defender, they’re rash, they make tackles they don’t have to.
"It’s really poor from Bailly, it’s so poor. Jose will hate what he’s seeing. All of them [the defenders] dive in, every single one of them. He will be absolutely fuming.
"You have to hang in there when you’re not playing well. The mistakes at the back. There’s no need to tackle, you’ve got to keep your composure.
"He’s complaining, winging, moping around."
Meanwhile, former Liverpool midfielder Graeme Souness faulted the 24-year-old for losing concentration during the encounter.
"His head is gone. Murray has got too much presence for him. Bailly doesn’t know if he's in New York or New Year. He’s in trouble here today," Souness added.