The Scotland international had been widely tipped to leave Old Trafford during the summer transfer window, with Fulham keen on a late move.
West Ham had also considered him before signing James Ward-Prowse and Edson Alvarez as Declan Rice replacements.
McTominay, however, stayed with his boyhood club and scored a dramatic late brace to turn what had looked like a crisis-deepening defeat to Brentford around on Saturday.
The midfielder has often borne the brunt of criticism during a difficult few years for United but has proven a different player for the Tartan Army.
His six goals during the qualifiers for Euro 2024 have taken Scotland to the brink of qualification, with only Romelu Lukaku scoring more.
Neville believes McTominay’s deep-rooted emotional connection to United mean he will run through “brick walls” for the club, as typified by his two late strikes on Saturday.
"The stuff I’ve seen on social media over the last few weeks, that’s when it’s the classic a club is falling apart when you start to have your fanbase and media people questioning the work ethic of a kid who has come through the academy,” he told Sky Sports.
"Sorry, I’m not having that. That’s one kid who will run through a brick wall for the club. That’s the weight on his shoulders and the pressure and feeling of completely not having the support in the club to be able to actually wear your legs down.
"I’ve talked about heavy legs in a young player, last season with Arsenal in a title run-in we saw it.
"What we’ve seen from Scott McTominay in the last few weeks is being outstanding for Scotland and then he comes back to play right of a diamond against Brighton and he looks like his legs have gone.
"All of a sudden you see clips on social media of him not running back. I wouldn’t look at that as anything other than pressure and carrying the world on his shoulders from being a Manchester United kid since the age of five.
"Saturday was a big moment for him and I was happy for a few of the payers that came back in because they’ve been battered and that’s what happens when you’ve got a club that’s failing. You end up not knowing who’s the good guys and bad guys. You end up calling [out] the ones that have been there a long time.”