The 19-year-old has been handed a key role by manager Roberto Martinez this season and has responded with a string of impressive performances.
That has helped him progress into the England senior set-up, winning his first cap last month and retaining his squad place for the national team's final World Cup qualifiers.
Barkley's rapid rise has attracted the interest of bigger clubs.
However Barry, on loan from Manchester City, has been able to watch the youngster at close quarters and believes a long run in the Toffees first team will be hugely beneficial.
"The manager has already shown he is not frightened to throw the younger players in if he thinks there is a role in the team and he thinks they have enough ability," said Barry.
"Ross is reaping the benefits at the moment and the more he plays the more confident he will get and the more he will improve.
"There are so many positives I can throw at him, for such a young player he is playing a very mature game.
"He is strong, quick, has a change of pace and the performances he has shown in the Premier League prove he can deal with the pressure.
"But on the other side the manager has already stated you don't want to put loads of pressure on his shoulders.
"You don't want to build him up too much. I think Everton is the perfect club to be learning his trade and the more he plays the more he learns and he will keep improving while keeping his feet on the ground, which will be ideal for him."
Barkley is set to return from international duty and go straight back into the side for Saturday's visit of Hull but fellow midfielder Steven Pienaar is unlikely to make that game.
The South African has been sidelined with a hamstring injury for the last month and is not quite ready to return.
"Probably Saturday is a little bit too early but I don't think he is going to be away for too long now," Martinez told City Talk.
"All the signs have been positive but we have to be careful we don't push him too early."
Martinez has been using the relatively quiet period during the international break to assess the squad members who have remained on Merseyside.
"We have to focus on the players we have here and it gives you an opportunity to look into the injured players and see where they are," Martinez added.
"Steven Pienaar and Antolin Alcaraz (hernia) have made huge progress and they are developing really well.
"We have eight players working every day and making sure they use this period as needed: some players need a bit of work, others need a bit of regeneration time and that has been really pleasing.
"On the other side you can look at the games and prepare the next period we have until the next international break but it has been very positive for everyone at the club."