Maccabi grabbed a late consolation through Roberto Colautti but Pulis was in no doubt the Potters deserved their victory.
The Welshman said: "I thought the lads were brilliant tonight. The balance looked good. The three centre-halves were very solid. There was a bit of a lapse at the end but that's a little bit of tiredness I think.
"I'm very pleased. They huffed and puffed a little bit but I thought we coped with it smashing."