Juan Mata grabbed the winner for United, his goal coming after Steven N'Zonzi had cancelled out an early opener from Marouane Fellaini.
Stoke did not give in, though, and were denied thrice in injury time as David de Gea produced two world-class saves to thwart Mame Biram Diouf and Marko Arnautovic late on, before Ashley Young's goal-line clearance earned United the points.
And despite his side struggling for a foothold over the remainder of the game, Hughes suggested his men deserved at least a point.
He said: "I think we deserved more on the balance of play. I thought we were very much in the game, certainly in the first half.
"We picked ourselves up after the disappointment of conceding early on and scored a really good equaliser.
"We were really encouraged at half-time because we felt there were rewards for us.
"In recent times, Stoke teams have come here and asked to be beaten but we didn't do that."
Hughes was also frustrated by the nature of the winner, with Mata's free-kick evading everybody and flying into the corner.
The Stoke boss felt the flag should have been raised for offside against Marcos Rojo, who initially claimed to have glanced the ball home.
Hughes added: "We were disappointed with the second goal because we think it was clearly offside.
"The lad Rojo is clearly interfering with play so the referee and the assistant should have cancelled that out.
"But we didn't allow it to affect us and we picked ourselves up. The saves at the end were unbelievable and it summed up our luck at the moment."
The win was United's fourth in a row, yet Hughes still feels the club he represented as a player are a long way from the form showed in their glory years under Sir Alex Ferguson.
He said: "This was never a game where we were consistently under pressure, like past visits here.
"I don't think United are at that level at the moment, but they have got the time and resources to get there."
