Giroud - who scored a first-half equaliser - was disappointed with the result, but he expects a positive response against Crystal Palace on Saturday.
“We did well in the first half and came back into the game after a bad start,” he told arsenal.com. “After the first half Dortmund were not as good, maybe tired, and we were really close to scoring a second one. But they kept going and scored on the counter-attack. It's a shame because we could have done much better.
“We finished the game better than them and that's why I'm really disappointed because if we couldn't win the game, we didn't have to lose it - maybe draw. In the Champions League it’s like that, about the details.
“I feel good. I'm used to playing a lot of games and I feel good with my body so touch wood no injuries. Over the years I've got used to playing a lot of games and I'm ok with my body. I don't want to find an excuse."
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