Sunderland have not had any enquiries for Pickford yet but are braced for bids this summer and Moyes heaped praise on him post-match.
Moyes said: "I had a joke with him afterwards, I don't think any of those saves were difficult!
"I said they are normal for you, don't start thinking you have done well because you made those saves! No, that gives you an idea of where I think Jordan is.
"I think Jordan is a big, big talent, I really do."
When asked whether Pickford can afford to have a season in Championship, Moyes added: "Jordan is under contract by us. That is the big thing. Good players, English players, have a really high premium.
"I have seen some of the rubbish figures in the papers, whoever came up with them was wrong.
"But we do know how good Jordan is and wherever Jordan goes - if he goes - then it would need to be a really, really big price.
"It would not be a cheap price if anybody wants Jordan Pickford."
Moyes compared Pickford to a young Joe Hart, who he'd considered trying to sign when he was Toffees boss.
"I thought Joe Hart developed and Jordan is well on that road at the moment. For me he has been the best newcomer in the Premier League, if you want to call it that."