Moyes said his side “could not have been more unlucky” as they crashed to their eight loss of the season.
Charlie Adam scored both goals – the first a deflected free-kick, the second a superb strike.
Robin van Persie got United’s goal.
“I don’t know what we have to do to win,” Moyes said after the game. “I thought we were extremely unlucky.
“We played well but for their first goal it was an incredible deflection and the second was a worldy.”
New mega-bucks signing Juan Mata, Van Persie and Wayne Rooney started together in United’s attack for the first time but the trio failed to create any clear-cut chances despite some good build-up play.
Stoke keeper Asmir Begovic did keep out Rooney’s injury-time free-kick with a flying save.
“We made numerous chances and opportunities to score, but we couldn’t take them,” Moyes added. “We should have been out of sight with the amount of opportunities we had today and we only have ourselves to blame.”
The loss leaves United in seventh, seven points behind fourth placed Liverpool and fans have taken to Twitter to vent their anger, using the hashtag #moyesout.
Sevan D said: #MUFC to be honest I’ve lost hope this season &next season. Hopefully #moyesout end of next year & maybe two years later MU can challenge.
It was the first time Stoke have beaten United in 30 years.
Image credit: Getty