The 22-year-old, who was one of the most sought-after central defenders last season, has seen his stock fallen following a disappointing season with the Toffees.
Campbell feels that England manager Hodgson should opt for Manchester United's Chris Smalling and Chelsea's Gary Cahill ahead of Stones at Euro2016 and has urged the youngster to avoid making mistakes if he wants to be given first-team responsibilities in France.
"I personally would go for Smalling and Cahill. I would go for the experience of those two guys," said Campbell.
"For me, something drastic would have to happen for Stones to start. You start with your most solid back four and go from there.
"If you keep making mistakes at international level, you're going to suffer because one mistake in a tournament and you can be out.
"If you make mistakes at a domestic level, you have more time to learn. He is learning.
"He just has to understand there are moments to play the ball and moments to keep hold of the ball. He just needs to find that balance."