Despite Everton being reduced to 10 men after 13 minutes when Idrissa Gueye slapped teammate Michael Keane, the Toffees snatched a 1-0 win over a United side who looked clueless on Monday night.
Amorim has used Shaw as the left centre-back in his three-man defence since the start of the season, and has slowly won the confidence of fans and pundits alike.
However, Neville is not convinced and the former fullback has torn into Shaw, who he thinks is nowhere near good enough.
"I'm not saying it's easy playing against ten men, you have to play with some urgency, you have to put as many players as possible forward, into forward areas. Shaw is starting to move forward a little bit, but he's ambling forward, let's be clear.
"You can't do that. You should be running forward every single time, I don't care. Yoro, I have more sympathy with because he's not as comfortable on the ball, but Shaw shouldn't be playing there. It's a waste of time, I don't care.
"Honestly, what he's doing there, you're not conning anybody."
The result ends United's four-match winning run at home and leaves them 10th in the table, above champions Liverpool. United miss the chance to move into the top four and will now use this week to prepare for their next clash against Crystal Palace, where Shaw may not feature.