Interim manager Ralf Rangnick suffered the first defeat since his appointment when Joao Mourinho’s late winner earned the visitors three deserved points.
United were second-best for long spells and could have lost by a heavier scoreline, had Wolves converted several chances during a dominant first half performance.
When Shaw was asked whether United’s defeat was down to them adjusting to Rangnick’s style of play, he said: “I don’t know, I’m not sure you can put it down to that.
“Us players, we have been here a long time, we’ve played at home, we know what it’s like when we have got that intensity.
“Maybe tonight we struggled, I didn’t feel when I was on the pitch that we were all there together. I think we felt like we were struggling and it was tough.
“You look at the players we have, we have unbelievable quality but sometimes quality is not enough.”
The defeat left United in seventh, four point behind fourth-place Arsenal with West Ham and Tottenham Hotspur also chasing Champions League qualification.
Rangnick could not guarantee that United would achieve a top-four finish after the Wolves defeat, admitting that there was much still to work on after this sixth game of his interim spell in charge.
“I cannot make any guarantees. Look at today's performance if I say we are 100% convinced we will finish in the top four I don't know if people will believe that,” he said.
“For me it is about taking the next steps and getting better. I knew this could be and would hard but today's game showed we still have a long way to go.”
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