The France international scored twice as Arsene Wenger's side drew 3-3 with Fulham at the Emirates Stadium on Saturday.
The double comes off the back of strikes against Reading in the Capital One Cup and Schalke in the Champions League in the past fortnight, and the striker has set his sights on a continued improvement.
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"I feel better and better," Giroud told the club's official website. "I'm confident about my qualities. I never give up. When I didn't score at the beginning of the season I stayed confident and always worked on my mind and my game.
"[The good form] is not a surprise for me. I want to play a lot of good games like tonight to succeed and to win a lot of games with my new club. I have to score and continue [to do so]."
The 26-year-old sympathised with midfielder Mikel Arteta, who missed a penalty in the final minute of the tie against Fulham, and backed Arsenal to turn their season around after registering just one win in their last four Premier League outings.
"It's a bad run but I think there is a lot of quality in this team," Giroud added. "We will have better days in front of us.
"I think Mikel wanted to score because he made a penalty against us. I think he really wanted to score.
"I was confident. Some guys asked me why I didn't take the ball but before the game the boss [has] a penalty list. It's very difficult because Mikel was under pressure because it's the last minute. It's not very easy to shoot a penalty."