United paid the price for missing numerous chances when Michael Lang poached a last-minute winner for Basel – who repeated their 2011 victory over them.
It denied United the point they needed to win the group and, bizarrely, leaves an unlikely chance of them not even qualifying for the last 16.
If they were to lose their final group game at home to CSKA Moscow by five goals and Basel beat Benfica, all three teams would finish on 12 points but Untied would go out on goal difference.
And Mourinho refused to blame Daley Blind for the last-gasp goal, saying: “It is not fair for Blind to blame himself.
“He had a very positive game. We have to blame everyone on the pitch because we had so many chances.”

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Mourinho could not believe his team had lost a game he said looked “impossible” to lose in the first half.
He said: “We lost because in the first half we should be 5-0 up but we could not score one goal after being so dominant.
“It looked for many periods in the first half it was impossible not to win. I think the majority of the second half the feeling of everyone was OK, it will be 0-0 but they got the late goal.”
As for qualification, he said: “Can someone help me with the maths?
“We don’t need to win the final match, we don’t even need to draw, it will come down to goals. But obviously we will try to win.”
The big frustration for Mourinho is that he will now not be able to rest key players ahead of the Manchester derby which comes five days after the CSKA game on December 10.
Blind admitted that he was at fault for the goal.
“The second half was up and down,” the Dutchman told BT Sport.
“It was a good cross and he came round the back and I was a little too late.
“We have enough confidence in the group, we will be well.”
United will only fail to reach the last 16 of the Champions League if they lose by more than six goals in their final group game against CSKA Moscow.
Should Basel match or better CSKA’s result, then they will be through.
United resume Premier League duties at home to Brighton on Saturday (3pm).