The England international has played twice for Arsenal since moving from Premier League rivals Manchester United late on in the transfer window.
Welbeck has not scored for the club since his switch and is yet to taste victory after a draw with Manchester City in the top flight and a 2-0 defeat to Borussia Dortmund in the UEFA Champions League.
Arsenal were second best at Signal Iduna Park as Jurgen Klopp's side overran the visitors on Tuesday, although Welbeck was among the chances and showed glimpses of quality.
While he failed to convert such opportunities into goals, Wenger maintains the 23-year-old will come good.
"He will [finish], I don't think we have to make a problem with that," he explained.
"He had a very lively first half and he couldn't finish from his two or three good chances in the first half.
"We have to be patient [with him]."
