Neville told Sky Sports that Maguire could follow in the footsteps of Marcus Rashford, who also went through a tough period at Old Trafford before regaining his confidence and his place in the starting XI.
"Harry is a good player and a good centre-back who has been brilliant at the last two tournaments - he's just had an awful time at United in the last 12 months and United is a very unforgiving place, I know that from being there for 20 years," said Neville.
"If something isn't right, that place can eat you alive, and Harry is just getting that at the moment.
"But I think he will come through it at United. Look at Marcus, he's been through a difficult period where he probably thought 'is my own club turning on me, is my own city not mine anymore? Do I need to move somewhere else?' But he's come out of it the other side.
"There are great players that I played with at United who went through the same sort of experience, where it was tough for them for a period. They came through it, were better for it and they're more resilient.
"I don't think Rashford or Maguire when they come out of this tournament will feel phased or lacking in confidence anymore."