The 20-year-old midfielder announced himself with a string of dynamic performances as Everton finished fifth last term, earning him a place in England's World Cup squad.
His direct running and spectacular goals drew widespread praise and admiring glances from some of Europe's top clubs, as comparisons were made to Liverpool captain Steven Gerrard.
Barkley committed his future to Everton in July, however, signing a new four-year contract, and now Jagielka says the Merseyside club have set the prestigious talent small goals to make an even bigger impact in this season.
"Our biggest challenge to Ross is to make those cameo moments into longer spells," the central defender told the BBC on Wednesday. "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."
Barkley made brief appearances in each of England's three group games at the World Cup and is widely considered the country's leading young talent.
Should he meet his club's challenges and add consistency to creativity, Everton and the midfielder can look forward to an even more exciting campaign than the last term.
The club enjoyed a solid first season under new manager Roberto Martinez, securing their highest league finish in five seasons and a Europa League spot playing an exciting brand of attacking football.
The Spaniard consolidated his squad in the close season, making permanent the signings of striker Romelu Lukaku and midfielder Gareth Barry, who were both loanees last term.
He also secured the long-term future of young talents Seamus Coleman and John Stones with new contracts.
Martinez said the new season, which starts with a visit to promoted Leicester City on Saturday, will mean a greater challenge to finish in the top four but retaining the services of Barkley is key to another successful year.
"Handing those players new contracts shows we have ambition, and it is something rare to have Barkley, who knows his best environment and he wanted to stay at Everton and carry on developing here," Martinez told Sky Sports on Wednesday.
"Sometimes to keep a player is more satisfying than signing one. It allows you to have continuity to face all the demands of the season with a strong backbone."