The Swiss midfielder’s discipline was once again called into question on Saturday when he caught Joe Allen with his elbow in the box in the first half in north London.
Charlie Adam duly stepped up to convert the resulting penalty from the spot and give the Potters the lead in the first half against the Gunners at The Emirates.
Xhaka is currently getting used to life at Arsenal following his summer transfer to the north London club from Borussia Monchengladbach.
The 24-year-old has picked up three bookings and a red card in all competitions for the Gunners so far this season.
And Kilbane believes that the midfielder must work on his discipline moving forwards.
Speaking to BBC Sport during the game, Kilbane said: “It looked like a penalty to me initially, because Granit Xhaka goes over the top on Joe Allen.
“Xhaka does something stupid every game he plays in.
“He’s on the edge for no reason.”
Arsenal return to Premier League action with a trip to Everton on Tuesday night.
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