Pickford has been criticised in recent times due to his erratic performances between the sticks at Goodison Park.
"One issue, of course, is the mistakes of Jordan Pickford," Rooney claimed in The Times.
"I'm sure Jordan knows, himself, that he needs to be much harder to beat. I still believe his attributes make him both Everton and England's best option and his errors aren't massive, technical ones — they are down to the mental side of things.
"The one little bit of advice I'd give Jordan is just calm yourself down. Take some time.
"With him, everything seems to be on a knife-edge, even to the point that when he's kicking it long it looks like he's kicking it as hard as he can — there was an instance, versus Liverpool, where he kicked it and nearly fell over afterwards."