Moyes felt it was vital his side scored first and was happy to see them hold out for a hard-fought victory to reach the semi-finals where they will take on Sunderland.
"I think the first goal tonight, whoever got it, was going to make a big difference," he told Sky Sports.
"It was a tight game, we had some good play at times but we hadn't created too many chances, but I don't think Stoke created too many either. I thought that once we got the first goal we were in control. When we got the second goal, we went on and saw the game out well.
"The conditions were a leveller, particularly in the first half it was really difficult for the players to play. The wind was blowing all over the place. Players will tell you that to play in heavy wind is as bad as anything."
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