Defender Robert Huth scored the only goal, turning Dean Whitehead's 15th-minute shot past Tim Howard.

Everton midfielder Marouane Fellaini should probably have had a penalty when he was man-handled by Ryan Shawcross in the area just before half-time, but referee Lee Mason did not see it.

The home side dominated possession after the break but, missing striker Louis Saha through injury, they did not do enough to force an equaliser.

"I'd be surprised if we didn't have a massive amount of the ball territorially but we never put in good balls or got anything on target," said Moyes.

"We were in good positions to create opportunities and we didn't.

"We huffed and puffed a little bit but I don't think we conceded many chances to Stoke.

"We weren't peppered and lost the game that way. We defended a corner but didn't defend the edge of the box and they get the shot and the flick in.

"We hadn't done an awful lot wrong and we found ourselves a goal down.

"I don't think we deserved to be behind in the game but we had to go chasing it.

"What wins games is goals and they got the goal and we didn't."

Everton's players were unhappy with the way Stoke scrapped and scraped to hold on to their advantage, with the Fellaini incident not the only one to have the home side complaining.

"I thought the referee had a poor game," said Moyes.

"It is not the reason for our loss - far from it because that was down to our inability to make and take [chances].

"But there was a lot going on in the box and we got very little of it.

"In the first half there were a couple of bear hugs on Fellaini, and I think if he had done it, we would have been getting all sorts."

Stoke boss Tony Pulis was delighted to register back-to-back Premier League wins with only their second away victory of the season - and only their second win coming immediately after a Europa League tie.

"This was a real battling performance against a good Everton team," he said.

"It has been a great week for the club. To get six points and to qualify for the latter stages of the Europa League is first class.

"We have had a dip of form, which most clubs do, and we have shown a lot of character and spirit the last week and the result (a 1-1 draw) on Thursday against Dynamo Kiev was a fantastic result for us."