The Czech midfielder gave an excellent, goalscoring display with the legendary Dutchman in attendance, while the Arsenal boss was pleased with his side's response
The influential Czech playmaker netted a contender for goal of the season on Saturday afternoon, with his clever dinked finish the culmination of a web of flicks and first-times passes.
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"I think we scored two great Arsenal goals. One of them being scored by Olivier Giroud, one of them by Rosicky," the French manager told reporters.
"I am very pleased for Rosicky, because today Bergkamp got the statue and I think Rosicky took on the role of Bergkamp today, because he scored a goal as well.
"Certainly Dennis would have been pleased to see him play."
Giroud netted twice before Rosicky grabbed Arsenal's third of the game on the stroke of half-time, with Laurent Koscielny also getting on the scoresheet – though Emanuele Giaccherini netted late on to end a run of 537 minutes without conceding a league goal at the Emirates.
After the disappointment of losing 2-0 to Bayern Munich in the Champions League, Wenger felt his side's convincing and comfortable win was the perfect tonic to a difficult week.
"We had a very demanding week, physically and mentally and we gave the right response today," continued the Arsenal boss.
"Against Bayern Munich, the target was to have a good performance and a good result. We had a good performance but were very frustrated with the result.
"But we had to transfer the positives from that game, and the belief, and overall we believe we'll still have a go at Bayern and we have shown today we are capable of responding."
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.Wenger confirmed that Koscielny picked up a back problem, Jack Wilshere has a tight hamstring and Nacho Monreal has injured his foot – though all three are expected to be available for next week.