The 20-year-old midfielder scored six goals in 34 Premier League appearances for Roberto Martinez's men last term before heading to the World Cup with England.
And Jagielka wants to see more from Barkley, but insists that Everton will be careful not to place too much pressure on the young star.
"Our biggest challenge to Ross is to make those cameo moments into longer spells," the central defender told the BBC Radio Five Live. "Then he will become a match-winner.
"We also want him to get a few more goals from that advanced midfield role he plays.
"We are setting him small goals but not heaping the pressure on him at such a young age."
Everton begin their Premier League campaign at Leicester City on Saturday.
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