The 23-year old joined Everton from the Black Cats for £30m, making him the most expensive British goalkeeper ever and the third most expensive of all time.
Tucker, who coached Pickford at the Wearside club, said of the transfer: "Yes, he's the third highest fee for a keeper in the world but if (David) de Gea, (Manuel) Neuer or the AC Milan keeper Gianluigi Donnarumma come on the market they would be £75million minimum.
"But, because of his age, Everton could get their money's worth and more.
"In goalkeeping terms, he's very young and will make mistakes and learn from them. It's about getting the overall consistency now. He's done it over a short period of 31 Premier League games, but the next challenge is to do it over two or three years.
"If he does that then he will be a regular for Everton and the plaudits and England side of things will come."