Alli has been out of favour for Mourinho this season but started in Wednesday's game. However, he was substituted after Stoke's 37-year-old debut goalkeeper Andy Lonergan thwarted him twice with smart saves.
It was Lonergan's first competitive game since turning out for third-tier League One team Rochdale in 2019.
"Yes, for me a player that plays in that position is a player that has to link and create and not to create problems for his own team," Mourinho said of Alli.
"In that situation, an objective counter-attack would probably end with a goal, and it ended with a counter-attack behind our defenders.
"We were unbalanced because when you are in possession you have full-backs out wide and another midfielder in a different line and they caught us in a counter-attack and they transformed the result of the game that was totally in our hands, so yes I am upset."
Bale was substituted at the break for Son Heung-Min for an apparent injury, although the Portuguese manager said the switch was partly tactical.
"I don't know. Something I think with calf. I'm not sure as at that time I just wanted to reorganise the team and make the change," Mourinho said.
Information from Reuters was used in this report.