Joao Moutinho’s superb strike saw the newly promoted visitors continue their strong start to life in the Premier League.
The Portuguese whipped in from the edge of the area as Nuno Espirito Santo’s team matched their hosts.
Wolves were lively in the first half and unlucky to go behind as Fred netted his first goal for United – the Brazilian firing in from just inside the box after Paul Pogba’s excellent touch.
And Mourinho said the visitors “were more aggressive, had more intent and were more motivated”.
“I think the result is fair. They deserved their point and we deserve the punishment of only getting one point,” the United boss told BBC Sport.
“The way we started we were lucky to be the first team to score. Their approach was more for a football match than ours.”
United, with former manager Sir Alex Ferguson watching on during his first visit to Old Trafford since having emergency brain surgery in May, were looking for a third straight league win.
The hosts were on top after the break, but Raul Jimenez’s clever lay-off set up Moutinho for what was a deserved equaliser for the visitors.
The draw keeps Wolves one point behind Manchester United in 10th, as Mourinho’s side climb to fifth.
The last time Wolves visited Manchester United in the Premier League, they fell to a 4-1 thrashing on their way to finishing bottom of the table. It was the same season Mourinho guided Real Madrid to a first La Liga title in four seasons.
Much has changed for both parties in the seven years since – Wolves dropping into League One before starting their ascent to the top flight and Mourinho making a title-winning return to former club Chelsea. But there was a sense of familiarity at Old Trafford as the well-acquainted Portuguese coaches took to either dugout.
Wolves boss Santo, Mourinho’s back-up goalkeeper for Porto from 2002 to 2004, regards his former manager as “a big inspiration” in his career, but he more than matched his mentor tactically as Wolves’ brand of quick, counter-attacking football caused the hosts problems.
Wolves were unlucky to head into half-time behind, with United goalkeeper David de Gea saving well from Willy Boly’s header having earlier parried a smart turn and shot from Jimenez.
The Championship winners have benefited from an influx of Portuguese stars under the influence of agent Jorge Mendes, who acts as an advisor to Wolves’ owners Fosun and also represents Mourinho.
And it was summer arrival Moutinho, with 113 Portugal caps to his name, who inspired the visitors’ fight back alongside his younger compatriot Ruben Neves in midfield.
Moutinho’s leveller was well deserved as Wolves became the first team this season to take points off both Manchester sides.
