After Charlie Adam's deflected free-kick had given the home side the lead, Robin van Persie restored parity early in the second half at the Britannia Stadium, and it looked like only one side would go onto to claim all three points.
However, Adam's thunderbolt just five minutes later was enough to earn Stoke their first league win over United since Boxing Day 1984, a result Moyes felt was not entirely deserved.
"I don't know what we have to do to win. We played well today," Moyes said.
"We lost to a wicked deflection from a free-kick and a worldy of a strike.
"The amount of opportunities and chances we created, we should have won the game.
"We only have ourselves to blame for not taking those chances, but I thought it was a good performance."
United's rhythm was disrupted on several occasions, as Jonny Evans and Phil Jones both had to leave the field with injuries, causing a mass reshuffle of the formation.
But Moyes was not using that as an excuse, admitting it had little effect on the match.
"We lost two centre-halves, which happens sometimes in football," Moyes added.
"But I don't think it changed the game as we kept going and doing the right things.
"Phil Jones looks like concussion, and has had a head scan, and Jonny Evans looks like he has a calf strain."
Winger Ashley Young also bemoaned a lack of good fortune on the day, insisting United were desperately unlucky not to have come away with something from the game.
"Of course we're disappointed to lose the game to a deflected shot and a goal out of the blue," he told Sky Sports.
"We've conceded two but look at the number of chances that we've created and the number of times we got to the byline and got the ball in the box but it just wasn't to be our day.
"I think it was a good performance and on another day we would have had three or four. We got to the byline plenty of times on plenty of occasions and it just didn't want to go in.
"Everybody's disappointed but we've got to lick our wounds and get back on with the job."
Juan Mata set up Van Persie for the United goal while Wayne Rooney went close to equalising for the champions from a free-kick late on, only to be denied by Stoke goalkeeper Asmir Begovic.
Young believes a fluid display from United's attacking trio is a genuine cause for optimism for the side going forward.
"It was nice to see Robin get a goal again and to see Juan play a big part in that," he said. "Wazza was fantastic. He had a few chances and he was fantastic again today.
"When he is on set-pieces he's always going to get it on target and the keeper has pulled off a world-class save (in stoppage-time).
"Even after that it has bobbled around in front of the goal and we've ended up with a shot that has gone over the bar.
"We'll take the positives out of the game and the amount of chances that we created and on another day like I said a few of them would have gone in."