The France international returned late to pre-season training having featured for his country at the World Cup in Brazil.
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"He had only three weeks rest, it was not an eternity and he had to come back quickly," Wenger told reporters.
"But sometimes when you come back late you want to work hard and in a game you are not as sharp.
"He's not put weight on, he's not out of shape, he's worked very hard this week and not recovered from the work he has done."
Giroud admitted to struggling with the pace of the game against the principality outfit, but insists he will be well prepared for the clash with City after another week of intensive training.
"It was really hard for me physically and I didn't feel really well in the game," he said.
"But it is okay as I have this week to work because we have to be ready for City.
"For pre-season preparation you have to work hard and there is less than one week to be ready."