The 19-year-old Toffees midfielder made his senior debut for the Three Lions during last Friday's 4-0 victory over Moldova in World Cup qualifier.
"It's too early," Kendall told the Daily Mail. "He has to be consistent at league level over a period of time and then be judged. It's too early now.
"A factor, of course, is the limited supply of players for the England team so they're wishing him on and it's quicker than it should be.
"They're jumping him forward because of the number of foreign players but the boy needs patience."
Barkley has scored one goal in four matches for Everton so far this season.