Saturday's reversal at the Britannia Stadium was United's eighth Premier League loss this season as a Charlie Adam brace either side of Robin van Persie's equaliser handed Stoke the points.
After Stoke's first league win over United since 1984, Moyes bemoaned the fact his players failed to make the most of the possession they enjoyed in and around the penalty area.
"I thought the performance was really good. I thought we played well," Moyes said.
"We created numerous opportunities, we played well (but) we didn't pick anyone out around the box. We lose to a free-kick from 30 yards with a wicked deflection and a worldy.
"I thought we were the better team. They get a goal, we get back in it, I thought we were the team more likely.
"I thought on the day we certainly did enough to get something out of the game."
United saw Jonny Evans and Phil Jones taken off injured in the first half. Evans has a calf strain and Jones suffered concussion after a tangle with Jonathan Walters.
A scan has since confirmed that Jones is "fine", according to Moyes, who felt United were unfortunate to be on the receiving end of a third successive away defeat in all competitions.
"We had bad luck, we really did," he added before lamenting some of United's decision-making.
"It was our own downfall that we didn't score our chances.
"We must have got to the byline eight, nine, 10 times but we never pulled the ball back or never picked someone out in the box so it's our own undoing."
