The Gunners forward believes that the club needs reinforcements if it is to challenge for major trophies this year, with Arsene Wenger's pursuit of Luis Suarez stalling.
The Gunners have only signed Yaya Sanogo this summer, on a free transfer, and have missed out on targets such as Gonzalo Higuain and Luiz Gustavo, though manager Arsene Wenger insists that he is pursuing new faces.
Luis Suarez has been the north Londoners' highest-profile target so far this summer but Liverpool has held firm after two bids, with Reds boss Brendan Rodgers declaring the situation "resolved".
Giroud told reporters in France: "In my opinion, it is important that the club signs another striker but it takes time, especially if it is a big-name player.
"I know what my job is and what I'm capable of. I just focus on myself and my ability. The manager is counting on me so I'm not thinking about [potential new arrivals] too much."
The Gunners' frustrations in the transfer market this summer were reflected in the atmosphere as Arsenal lost 3-1 to Aston Villa on the opening day of the Premier League, with the club's Supporters Trust and the Black Scarf movement both writing to the board in concern.