A comfortable 3-0 win over Arsenal on Sunday has moved Everton to within a point of the Gunners, and Barkley insists that the Toffees will be confident of earning victory in each of their remaining six games.
"You saw against Arsenal that we can play, and that we're good enough to be in the top four," the midfielder told reporters. "On our day, we can beat anyone.
"Now we have to go into every game thinking we can get all three points.
"We've got confidence now, and we have to take that into our remaining games."
Roberto Martinez's side take on Sunderland at the Stadium of Light this Saturday.