Former Arsenal striker Robin van Persie scored the only goal of the game in the first half at Old Trafford to condemn Arsene Wenger's side to only their second league defeat of the season.
But at the end of a week that saw the Londoners defeat Liverpool and Borussia Dortmund, Wilshere is keen to keep things in perspective.
"It's frustrating but we always seem to come here and dominate at times," Wilshere told Sky Sports.
"At the end we had some good chances but it's frustrating we didn't get a result.
"We are still top of the league and we have to go away from here, clear our heads and prepare for a god game at home against Southampton and hopefully we can push on from there.
"We had a good week overall. We beat Liverpool and Dortmund away and there are not many teams can do that.
"It's a tough ask to come here and win, they are a strong team, so we have to look back at the week and take the positives."
Wilshere feels Premier League sides respect them more in the wake of their positive start to the campaign.
But he admits he is frustrated at having to settle for a bit-part role so far, as he battles back from an ankle injury.
"We've had a strong start (to the season) and teams fear us now but United did well today and showed good spirit," he added.
"I want to play every game but it is about being patient. I wouldn't say I am 100 per cent match-fit yet, so I am looking to get a few more games under my belt."