The Red Devils failed to guarantee themselves a place in the Champions League last-16 with a surprise setback on Swiss soil.
They remain top of Group A and in a strong position to progress, but once again struggled to shake the shackles which held them back during Pogba’s recent injury-enforced absence.
The Frenchman has returned to the fold in United’s last two outings, but was replaced 66 minutes into the Basel clash by Nemanja Matic and Mourinho admits his team unexpectedly crumbled after that to see Michael Lang snatch a dramatic winner .
“Did Pogba coming off have an impact on the team?” the Portuguese mused to reporters after suffering a rare European reversal.
“I think it did have an impact, we were not such a good team after Paul came off but it had to be with the levels of fatigue after 65 minutes.
“I brought to the pitch an experienced player like Matic and thought it couldn't affect the game.
“I bring Marcus [Rashford] to give us more speed, more problems to them, Zlatan [Ibrahimovic] to hold the ball and the approach was good.”
Mourinho had previously conceded to BT Sport that his side’s inability to convert chances also cost them dear .
He said: "We lost because we should have been 5-0 up at half-time and could not score after being so dominant.
"We were in an easy way for many periods — it looked almost impossible not to win.
"But experience tells you that when you miss so many chances you put yourself in this position. In the second half, maybe we think the position at 0-0 was okay, but then they score the last minute."
United are set to play host to CSKA Moscow on matchday six, with a point enough to take them through as group winners.
Prior to that contest, Mourinho’s men have Premier League fixtures to take in against Brighton and Watford.
They also face a trip to Arsenal on December 2, while a derby date with Manchester City awaits after they have taken on CSKA in what is shaping up to be a potentially defining period in their season.