A disappointing 2-0 loss on Wednesday ensured Arsenal will have a mountain to climb in the second leg of their Champions League last 16 tie in Germany, but there was no sign of a European hangover as the London club dominated Sunderland.
A near-perfect first-half performance, featuring two goals from Olivier Giroud and a well-worked team move finished off by Tomas Rosicky, put the hosts in complete control of the game.
Arsenal took their foot off the gas a little in the second period but Laurent Koscielny added a fourth prior to Emanuele Giaccherini's late consolation.
Wenger hailed his side's strength of character after seeing them move back within a point of leaders Chelsea, victors over Everton in Saturday's early game.
"Against Bayern, the target was to have a good performance and a good result," he said. "We only had a good performance.
"We were frustrated with the result, but we had to transfer the positives that we got from that and we showed today that we could respond.
"We had a very demanding week, physically and mentally, and we gave the right response. We did the job in the first half and scored two great Arsenal goals."
Wenger insisted he had no doubts in recalling Giroud, even though the Frenchman had not scored at home in the league for six games and had been the subject of newspaper reports surrounding his private life.
"I had no hesitation about his strength of character," Wenger added. "He scored two goals, one a great Arsenal goal and one a gift from Sunderland.
"He did well; I had no doubts (about him)."
