Despite the comfortable margin of victory, Mourinho rebuked his team for taking their foot off the pedal.
“Until 2-0 we were very stable,” he said. “After 2-0 everything changed. We stopped playing seriously and stopped making the right decisions. We could have put ourselves in trouble.
“We were playing fantasy football, PlayStation football. I don’t like it.”
Basel had previously proved a thorn in United’s side, eliminating them from the Champions League in 2011-12, and they inflicted a surprise defeat upon Mourinho in the first European game of his second Chelsea stint in 2013.
While Raphael Wicky’s side were pushed aside without too much fuss in this Group A opener, Pogba’s premature exit with an apparent hamstring injury meant Mourinho could not reflect on an entirely satisfactory night.
With Ashley Young coming into the United XI at right-back in place of Antonio Valencia to make his first start of the season, Pogba inherited the captain’s armband from the Ecuadorian.
But the Frenchman’s debut as United skipper would last just 18 minutes after he abruptly clutched the back of his left leg and was obliged to hobble off in disgust, with Fellaini joining the fray.
Lukaku opens his account
United had been getting on top and they went close to taking the lead when Henrikh Mkhitaryan jabbed Lukaku’s low cross against the post and then saw his follow-up smothered by goalkeeper Tomas Vaclik.
Luca Zuffi gave the hosts a scare when he sliced wide in front of the Stretford End after Chris Smalling failed to deal with a high ball, but two minutes later United opened the scoring.
The home fans could have been forgiven for wondering if it was still 2015, when the stadium last hosted a Champions League game, as Young sidestepped Blas Riveros and whipped in a perfect cross that Fellaini headed home.
Quiet in the first half, Anthony Martial came to life early in the second, beating Manuel Akanji and Taulant Xhaka before dispatching a skidding shot that Vaclik turned behind.
The resulting corner, taken short, yielded United’s second goal as Daley Blind’s drilled cross was emphatically headed in at the back post by Lukaku, who notched his first goal in the tournament proper.
Frequently maligned for his ungainliness, Fellaini by now was running the show, freed to roam forward by the anchoring presence of Nemanja Matic behind him.
Martial should have made it 3-0 from the Belgium midfielder’s cut-back midway through the second half, only to steer his shot off-target from close range.
Lukaku and Young both worked Vaclik, while Mohamed Elyounoussi tested David de Gea’s concentration at the other end after cutting inside the sliding Victor Lindelof, before United did claim their third in the 84th minute.
Mkhitaryan completely miscued his attempt at a side-foot finish from Fellaini’s right-sided cross, but substitute Rashford followed up to scuff a shot into the ground and over the despairing Vaclik.
Off the pace domestically, Swiss champions Basel have now gone nine European games without a win.
“I’m very disappointed with the result,” said beaten coach Wicky. “But I would not say I’m disappointed with my team.”