"No, I'm not satisfied with a point because we were the team closer to winning", he said via his club's site.
Eric Bailly's lack of positional assurance led to Jean-Eric Choupo-Moting scoring Stoke's opener before a slip from Phil Jones allowed the Cameroon worldwide to claim his second six minutes after Romelu Lukaku put the visitors ahead.
Just over 10 minutes into the second half, United took the lead as Henrikh Mkitaryan played in Lakuku, who was denied by Butland initially but managed to slot home the rebound. However, at the brink of half time, United levelled through Marcus Rashford.
P.S. Individual mistakes may have marred United's game but one moment of quality stood out in sharp relief: Let's close the book on save of the season already shall we?
"We will always try and go up against teams", Hughes said.
Both keepers pulled off excellent saves late on as the action pinged between both areas and Lukaku should have done better when close in on goal with nearly the final kick of the game.
The Cameroonian global played an integral part in a frenetic encounter, scoring his first Potters' goal and breaking the deadlock in the 43 minute; sliding in ahead of the visiting defence to finish off a fine passing move from six yards after great work from Darren Fletcher and Mame Biram Diouf.
Mourinho blamed the worldwide break for a United showing that failed to match the high-octane performances that preceded it.
Mourinho confirmed that he shared this line of thinking by saying: "It was a hard match for different reasons". One team tried to win, one team tried to get the point but they fought hard to get that point.
Following the draw, Stoke City now occupy the tenth league spot with five points, and are set to face Newcastle United on September 16. It was United who took the lead then.
Chelsea had a 2-1 win away to Leicester in the meeting of the previous two seasons' champions.
Danny Welbeck scored twice as Arsenal returned to winning ways and condemned winless Bournemouth to a fourth successive defeat.
Brighton scored its first top-flight goals in 34 years in a 3-1 victory over West Bromwich Albion.
United won a risky free-kick when Allen fouled Juan Mata on the right-hand side of the area but the Stoke wall held firm, and Butland made a fine reaction stop from Jones' late header and Pogba hooked a half-chance over in the final seconds.
In the day's other game unbeaten Watford moved above Southampton and into the top four by beating them 2-0 with goals by Abdoulaye Doucoure and substitute Daryl Janmaat.