Celtic forked out £5m plus add-ons to land the shot-stopper from Greek side AEK Athens in the recent transfer window and boss Neil Lennon has been looking for Barkas to make a big impact between the sticks.
The custodian has split opinion however and Stewart is of the view he is yet to show he is goalkeeper that Celtic need.
The former Scotland midfielder feels that Barkas has yet to stand up and show he is capable of pulling off big saves when Celtic need them most.
He said on BBC Sportsound: “Barkas has not stood out for me.
“Compare him to Fraser Forster or even Craig Gordon.
“He hasn’t shown he can make the big saves they can yet.”
Barkas conceded three at Celtic Park on Thursday night as AC Milan inflicted a 3-1 loss on the Scottish champions in their Europa League group stage opener.
Celtic were linked with a host of goalkeepers over the course of the transfer window, but opted to splash the cash on Barkas.
The goalkeeper has been capped 12 times at international level by Greece.