The on-loan Barcelona forward netted the opening goal in the Toffees' 4-0 win over Stoke on Saturday.
Barry accepts Deulofeu still has plenty to learn about the English game but predicts the 19-year-old's progress will improve with more games behind him.
"We have seen it all season in training but he's had to be patient and wait for his chance because a lot of other players have been doing well too," said Barry.
"He is so difficult to mark one on one, he loves getting at players and has a lot of pace and he made it difficult for his full-back (Erik Pieters).
"You can give yourself a yard but he has the pace to make it up. He will be difficult to play against and the more he gets his chances I am sure he will improve again.
"Anyone who has come through their (Barcelona's) ranks is going to have some real quality about them: the fans are starting to see that now and I am sure there is more to come.
"There is still a lot that Gerard will have to learn coming up against different opposition but it's been a fantastic start for him."
Deulofeu's selection and Leon Osman's return to the side saw Kevin Mirallas and Ross Barkley dropped for the Stoke game.
Everton now look as though they have plenty of options, not only player-wise but in terms of their flexibility, as late in the game Martinez switched to a back three - which was his preferred formation at Wigan prior to his summer move to Goodison.
"The bench was really strong and if things hadn't gone to plan we had a lot of options and that's a positive," added Barry.
"I am sure the team selection against Stoke was looking at the games ahead (Everton face Manchester United and Arsenal in the next week) so everyone will be needed in this busy period with a lot of games this month.
"Everyone will have to be ready to take their chance when it comes.
"I think it is good that the manager can look to not only change personnel but formation too.
"It is good that you have another option; we went to five (in midfield) to finish the game and we looked comfortable."