Giroud almost found a winner late on against the Potters with an audacious effort from distance, but saw his effort fly just over with goalkeeper Asmir Begovic beaten.
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"I hoped [my shot] would go in," he told the club's official website.
"I saw the keeper off his line and I did not see Aaron [Ramsey] for a cross. So I tried to take my chance.
"[It means] we have to wait for our [first] victory. But it is coming soon. We played well and had some good situations in front of goal. We just have to score now - me too.
"But I gave it my all. It was a hard game against a big team. But I felt good in the game and we missed one little thing - a goal.
"But there are a lot of good players here at Arsenal. It is easy to play with them. We need a little more time to come together."