The Red Devils saw their 100% start to the season ended by the Potters at the bet365 Stadium courtesy of an Eric Maxim Choupo-Moting brace, cancelling out goals from Marcus Rashford and Romelu Lukaku.
Mourinho claimed that the international break had an effect on his side's performance, but still believes that United were closer to winning the match than losing it.
"It was a difficult match for different reasons. My players, after the international break, are not the same," he told BT Sport.
"They weren't performing at their normal level but we were in the game, we fought hard and we were closer to winning than losing.
"Stoke are big, strong and powerful in the air. They fought hard and probably deserved a point. A point is a point. It is not what we came for but a point is a point."
Mourinho also told BBC Sport: "No I'm not satisfied with a point because we were the team closer to winning. I have to say it is a result I accept though.
"One team tried to win, one team tried to get the point but they fought hard to get that point - they defended well, they counter-attacked and in set-pieces they are powerful."
United will now turn their attention to the Champions League, where they host Basel on Tuesday.