The Manchester United legend has opened up on the pressure that has been building on the shoulders of his former team-mate, despite recent wins over PSG and RB Leipzig in the Champions League.
Those victories have been blighted by defeats against Tottenham, Arsenal and Istanbul Basaksehir - making the trip to Goodison Park a rather nervy one for Neville.
The Sky Sports pundit has admitted that he was glued to the TV for a full hour before kick-off.
"I was glued to the telly from half past 11 [on Saturday] morning," he told The Gary Neville Podcast.
"I was thinking about the game, thinking about results leading up to the game, thinking about reports earlier in the week and thinking this needs a performance here.
"Ole Gunnar Solskjaer needed a performance, the club needed a performance, those players needed a performance.
“I think United deservedly came out on top in the end. They're just inconsistent.”
Former United striker Solskjaer was quick to question the 12:30pm kick-off time following the 3-1 win, and he even alleged that his team were set up to fail.
He told BT Sport: "We were set up to fail. The kick-off time set us up to fail.
"We have been to Turkey, played loads of games this season already, we got back Thursday morning and we are playing Saturday lunchtime, it's an absolute shambles. These boys deserve better. Luke Shaw has got injured because of it.
"It's a hamstring which might be a long one and Marcus Rashford might be struggling.
"The authorities set us up for fail, who is responsible? We've had enough of that.
"Players this season, in these times, a pandemic, mentally and physically it's draining.
"Let us play on a Sunday, there's an international break after this, it's a joke.
"The players were brilliant. Cavani is getting better and better."