The 26-year-old has found the target just once in nine competitive matches for the North London club so far this season.
"People say to me 'the goal is coming soon, don't worry, we trust you'," he told Eurosport. "It is very important for me to feel the support of people and my teammates too, so I think we are good.
"We lost against Chelsea but I think it's an accident and we are confident for the future. Me too, I am confident and I want to keep going.
"Don't worry about the future, the goals are coming soon. It's like when you score one, you take confidence and more trust, you know. So, it's like that when you're a striker. You need to score but I'm not worried about that."
Giroud added that once he breaks his duck in the Premier League, it will be easier for him to score frequently.
"[Arsenal manager Arsene Wenger] says sometimes I feel the pressure a little bit but I'm not worried about the pressure," said the Frenchman.
"I want to play and take a lot of pleasure on the pitch and we won [against Olympiacos in the Champions League on Wednesday] so it's okay.
"Like you say, when I score my first goal in the Premier League, although I scored in the cup, it will be better and better."
Giroud joined Arsenal from French champions Montpellier in the summer.