The Frenchman scored his first Premier League goal for the club in the Gunners' 3-1 victory against West Ham on Saturday.
Prior to that strike Giroud had failed to justify the hype since his €15 million move from Montpellier in the summer, and he has revealed the task of filling the void left by the Dutchman has affected him.
"Van Persie is now gone, there are many expectations about me," he told RMC.
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"It is clear that this goal [against West Ham] is important for me. Especially before the international break, it gives me confidence, even if I had been decisive four times before.
"I am very well integrated. If I didn't score before, it was essentially a problem of effectiveness or success. It happens sometimes, periods like that, for any striker. In this case, we must continue to work.
"I never doubt. I was facilitated by the support of my team-mates, fans and of course the coach.
"He talks to me from time to time. I was put in trust, and it makes me feel good and I feel I'm progressing every day."
Speaking to Canal Plus of his strike at Upton Park, he added: “When I saw the ball go in the net, that was what I was waiting for, it was a baptism [in the Premier League] and I hope there will be lots more goals.
“I expected it to be difficult at first because the Premier League is a league you have to adapt to. A lot was expected of me and I had to deliver immediately which is why I was frustrated.”
Giroud believes he has been unlucky so far in his Arsenal career, and hopes his goal against West Ham will be the catalyst for a change in fortune.
“Last week against Chelsea, I did what I could but [goalkeeper] Cech did well, I was ‘close’ as they say there [in England],” he added.
“But it is nice to have scored my first goal. It will give me a lot of confidence for the future. I feel good about this team and I am confident that I will score more goals. Perhaps even a dozen like my first season at Montpellier."