Rojo, meanwhile, is back after seven months out with a knee injury and made his first start of the season.
The United manager added:"The first half the attitude was good, the football was good, is really diff to blame just football, easy match to win and then you lose, great for them, they have a good chance to qualify".
A point in Switzerland would've guaranteed progression, but after squandering a host of good first half chances, Basel grew into the game after the break, eventually finding a 90th minute victor through Michael Lang.
"We lost because in the first half we should be 5-0 up but we could not score one goal after being so dominant", Mourinho told BT Sport. Should they avoid a four-goal defeat, qualification is guaranteed.
They arrived in Switzerland needing just a point to guarantee top spot in Group A and the same scenario will be in place will be the same again when CSKA Moscow visit Old Trafford on December 5 although, in truth, only a seven-goal defeat will see Jose Mourinho's side fail to go through.
However, United didn't seem bothered when they pieced together a sweeping move that nearly brought an early opening goal.
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McCoy's 27-yard run in the first quarter tied the score at 7, which was on the heels of his 37-yard scamper. LeSean McCoy was the lone bright spot for the Bills , rushing for 114 yards and a score on 13 carries.
Fellaini threatened again with another header that fizzed wide from Daley Blind's free-kick.
Paul Scholes, meanwhile, said Pogba's unavailability explained why Romelu Lukaku had suddenly gone off the boil.
Martial was denied by Vaclik at the end of a surging run before Rojo rattled the bar from long-range. Mourinho threw Marcus Rashford, Nemanja Matic and Zlatan Ibrahimovic in from the bench, but it was Basel that were forcing matters.
It was his second appearance since returning ahead of time from a hamstring injury which ruled him out for two months. David De Gea did wonderfully so far this season and he got a night off. Manchester United will host Brighton this coming weekend as points in the Premier League are a priority now.
Even Ibrahimovic couldn't help United stem the tide and Basel's pressure was finally rewarded in the 89th minute.