Barry believes the Toffees are entering an exciting new era at Goodison Park, provided the 'Fab Four' can continue to fulfil their potential.
"I can't think of four better young players at the same club, when you are talking about four regular starters who are consistently producing," Barry said.
"They are scoring goals, making assists and you can tell with the aura they've got on the pitch how much they are enjoying it.
"Of course, they need to keep learning along the way but it is important they don't lose that swagger.
"I'm not going to build them up too much but if they keep performing the way they are, they will be special players."