Stones was hammered for his performance in England's defeat to Holland last week.
"We gave John Stones a lot of criticism and attention after the game the other night," Neville told Sky Sports.
"I have got a lot of time for John Stones. I have thought a lot about it in the last few days. It is a good time for him for the summer to be coming. If I were John Stones I would spend a lot of time thinking this summer about how I am going to attack next season.
"We talked a lot the other night about playing out from the back. I actually think John Stones has got to become a great defender and with that there becomes a real seriousness about how you are on the ball.
"He is very relaxed on the ball. That's good, it shows composure. But then you have to be able to flick that switch and get that competitiveness into your defending.
"I don't know if he has watched Gerard Pique in the last five to ten years or done analysis of a player that he would like to be like but for me if you look at Gerard Pique on the ball and then within a second showing that aggression and aerial ability off the ball.