The Potters appeared to be heading for a third consecutive Premier League win and a third against United within four home league games until Wayne Rooney's late intervention deep into time added on.
The United captain, who came off the bench on 67 minutes, bent a 94th-minute free-kick beyond Lee Grant to become the Red Devils' record goalscorer and preserve United's unbeaten run to 17 games in all competitions.
That cancelled out Juan Mata's own goal at the other end which came in the first-half after Erik Pieters' low cross diverted off the diminutive Spaniard and got the better of David De Gea at his near post.
But though United dominated much of the game and arguably earned a deserved draw, Hughes felt Clattenburg and the match officials were wrong to add on as long as they did at the end.
Stoke boss left bemused by decision to add on five minutes
The Welshman told the media afterwards: "From our point of view, I thought we worked exceptionally hard. We put a great shift in, in terms of effort and trying to get real shape and make it a difficult day for United.
"I thought we started really brightly and in that key period then obviously we created a moment that allowed us to get a goal on the board by creating a mistake in their back line, so we were grateful for that.
"Second-half we found it a little bit difficult I have to say to just get a foothold in the game, in terms of what we wanted to do. Sometimes you have to credit opposition for pressure that they put on you in terms of not giving you time on the ball.
"There was a few occasions when we could have been a little better in possession and taken the ball and played a little bit more in the opposition half in that second-half.
"I'm still scratching my head a little bit, in terms of where the referee got the five minutes from. The sooner they get somebody in the stand with a stopwatch to take the time-keeping away from the referees, the better in my view. But that's for another day.
"You get to that late stage in the game and you think you're going to win it, but obviously when you concede it feels like a defeat. But we'll wake up in the morning and realise that we've had two games against United home and away and we haven't been beaten this season, so we'll take credit for that."
We'll take the positives of having not lost to this United team, declares Welshman
Rooney completely re-wrote the story of the game with his late equaliser, one which means he has now surpassed Sir Bobby Charlton to have scored more goals than anyone else for United with 250.
It looked as though Stoke would be rewarded for their efforts with another three points at the Bet365 Stadium against United, before Rooney's late effort denied them at the death.
On Rooney's subsequent achievement, Hughes continued: "Yeah, it's unbelievable. Sir Bobby's record has stood for 40-odd years so it tells you how typical of that [it is].
"A lot of good strikers have been and gone in that time and not got anywhere near it, so for Wayne to do it - clearly we didn't want it to happen today, that wasn't the plan we had - but you have to say he's done that throughout his career.
"You only have to give top players one opportunity and that's what he had. He had to produce a ball that was right on the money, and that's what he's done.
"United players and teams have done that for many, many years right at the death to win games and get something out of games at that late stage when you think a game's slipping away from them."
Asked about how he gauges United's current team, having played for United for seven years and scored 116 goals in 352 appearances, Hughes added that they are "a very good team who are playing very well."
"They've kept their run going again," he said. "There's not too many teams in the last 3-4 months - whatever it is since they've been on this run of form - that have been able to take any points off them. Ourselves and Liverpool, clearly. We'll take the positives from that.
"They're a good side, they've got good talent and towards the end of the game today, they were able to bring fresh legs on with pace and power.
"You've got to try and match that and keep them out. We did that up to a point but clearly the little bit of magic from Wayne has got them something out of the game."
Rooney in 'good company' among list of former United strikers, says Hughes
But Hughes refused to suggest whether Rooney is the best striker ever to have played for his former club.
He added: "It's difficult to compare players from one era to the next, to be perfectly honest.
"In terms of the impact he's had at Man United, it's been huge. He's won almost every trophy that's available, goalscoring records are falling now, and he's right up there.
"It's a heady mix in terms of the quality of players that have pulled the shirt on but he's in good company, let's put it that way."