Wenger's side passed on the chance to reclaim top spot in the Premier League as Arsenal dropped points against United at the Emirates Stadium.
But the Frenchman was understanding after seeing his side turn in a cautious display against the defending champions, with their 5-1 hammering at Liverpool on Saturday in mind.
"It is not worrying because we care about what we do and when you concede five goals like we did on Saturday, we are only human beings," said Wenger.
"Sometimes you don't score because the team was highly focused not to concede.
"I felt we were nervous, yes.
"Where we are usually very dangerous breaking through the middle with speedy passing, Man United defended very well there.
"We got plenty of crosses in and their experienced players, people like (Nemanja) Vidic and (Rio) Ferdinand in the second half, did very well with that."
Arsenal have the opportunity to gain immediate revenge on Liverpool when the sides clash in the FA Cup on Sunday before Wenger's men welcome holders Bayern Munich to the Emirates in the UEFA Champions League last 16 on Wednesday.
Wenger added: "We have come out of two difficult games and are still in a strong position.
"That is the only positive. We had two bad results, but we are still in a position where we can do it."
