The France international squandered a great opportunity to score and secure three points for the Gunners when he fired wide from close-range late on after coming on as a second-half substitute.
Giroud insisted he also made a slow start to his Montpellier career before becoming a prolific goal scorer for the club – and he is confident he can do the same at the north London outfit.
“This could have been the dream start,” Giroud said. “But in Montpellier, I did not score for my first game, so I am not worried. Here, I will have plenty of chances and I will score.
“Last season was wonderful here for Robin [van Persie], but before that, he took time to settle. I am just asking people to be a little patient with me.
“I am not here to make people forget Robin, because he has made beautiful things here, but I just want to bring something new.
“However, I am under no more pressure than that, because if I think about that when I go onto the field, I will play with the handbrake on.
“I know Arsenal is a great club and needs a striker ready and efficient quickly. I need games to get confidence, and it is up to me to succeed.”
Arsène Wenger also backed Lukas Podolski to be a success at Arsenal, despite the German struggling to conjure any efforts on the Sunderland goal at The Emirates.
“I see him as a centre-forward, but he has some work to do, to change his game a little bit, make runs in behind to protect the ball and move around the box,” Wenger said.
“When you come from a wide position, it is not easy to do that, but he will get there. He is a fantastic finisher, but had no real opportunity.”
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