The Gunners opened their Champions League Group D campaign with a deflating 2-0 defeat - but it could have been five or six.
Three days after missing a golden chance against Manchester City's Joe Hart, Welbeck failed to covert a one-on-one with another goalkeeper - Roman Weidenfeller.
Welbeck's record in front of goal has been criticised but Wenger defended his £16m signing from Manchester United.
Wenger said: "Danny will improve, I don't think we have to make a problem of that.
"He had a very lively first half. He had two or three good chances but couldn't finish them. There was one obvious one. We have to be patient with him.
"The paradox of the night is that we had very good chances to score first, but they then scored from counter-attacks."
Arsenal's defending was woeful and Dortmund would have won by a landslide but for the reflexes of Wojciech Szczesny and their own wastefulness.
Wenger was scathing of the performance and admits his players had under-performed across the pitch.
He added: "We lost the ball at the throw in but it was still three against Immobile at the back.
"It's still difficult to understand how we concede the goal. There were still enough people to stop the goal.
"Dortmund were very strong in midfield. They were stronger than us in midfield.
"But it's very difficult on the night to go into any individual assessment of any player because as a team we were not at the requested level.
"It was a difficult night. Dortmund were the better team. Our performance was disappointing."
To complete a dispiriting night that has left Arsenal's transfer policy and Wenger's team selection open to criticism, Jack Wilshere limped off with an ankle problem.
"Wilshere has turned his ankle. It's difficult to say how bad it is because I'm being cautious," Wenger said.
"Normally it's not very bad but because of his history [with ankle injuries] I'm being cautious."
