The Red Devils dominated the game, but despite the creation of a number of chances, it was not until the second half that they managed to take the lead through Anthony Martial.
The hosts pressed on to kill the game with a second goal, but they failed to hit the back of the net, and Joe Allen netted a late equaliser to rescue a point for the Potters – who remain without a win this Premier League season.
Despite Allen’s goal, it was teammate Lee Grant who was named man of the match following an excellent showing in goal, in what was only his second top flight appearance.
He frustrated United time after time, and Mourinho believes it was unfair Stoke managed to claim a point after such an attacking showing by his players.
The Portuguese coach said: “We showed a great attitude, because after the 1-0 the team wanted to kill the game; they were feeling so confident and kept creating chances.
“But then by magic they cross the midfield line and score a goal, which was very unfair on us.
“I never criticise my players for missing chances; the goalkeeper is man of the match, obviously deservedly.”
The performance was arguably the Red Devils’ best of the campaign, perhaps topping even the showing put in against Leicester last weekend, and Mourinho bemoaned the inability to secure a ‘fat result’ against the Potters.
“Very good performance I have to say,” he added. “In this moment we should be not just with the three points but we should be with a fat result.
“But we go with one point.”