The Frenchman has made a slow start to his Gunners career following his £13m move from Montpellier in the summer, and has found himself under pressure to replicate the goals of last season's top scorer Van Persie.
However, Giroud is adamant that he needs some time to settle and is confident that the goals will come.
"Everywhere I've been, I've needed some time to adapt, but in the end it's been really good," he told Le 10 Sport.
"I'm a level headed person who needs something to aim for to move forward, but I haven't given myself the task of replacing Van Persie.
"I want to take my place, win over the Arsenal fans in my own way."
The 25-year-old finished as the Ligue 1 top scorer last season.