Podolski came off the bench to net a 91st-minute winner as the Gunners produced a remarkable comeback to beat Anderlecht 2-1 in Belgium tonight.
It was the 29-year-old's first goal in a season where the Germany international has struggled for first-team opportunities, resulting in speculation over a January move.
"We know Poldolski can always score. He is frustrated and I understand that of course," Wenger told The Mirror.
"But he's important as well and he showed that tonight and he will be important in the coming months.
"He was never close to leaving in the summer. He has 115 caps for Germany that is not a coincidence, that shows you the quality."
Wenger's side looked down and out when Andy Najar struck on 71 minutes to give the Belgian club an unlikely lead at the Constant Vanden Stock Stadium.
However, Kieran Gibbs pounced with a 89th-minute equaliser, before Podolski completed the turnaround shortly after to spare Arsenal's blushes.
The German is contracted to the Emirates Stadium club until summer 2016.