The France international looked laboured in the Gunners' 1-0 Emirates Cup defeat to Monaco on Sunday - a result which saw Valencia win the pre-season tournament.
Having seen fellow forwards Yaya Sanogo and Joel Campbell light up the Emirates on Saturday, with the former grabbing four goals in a 5-1 victory over Benfica, Giroud's performance was nowhere near as eye-catching.
The 27-year-old scored once in five World Cup appearances for France as Les Bleus lost to eventual winners Germany at the quarter-final stages.
And, although he admits he is struggling for fitness following an extended season, Giroud believes he will be much sharper in time for Sunday's Community Shield clash with Manchester City.
"We did well on Saturday and had a great game, scored a lot of goals but on Sunday there was another team who have had only three or four days of training," he explained.
"We could see it, especially for me - it was really hard for me physically and I didn't feel really well in the game but it is okay as I have this week to work because we have to be ready against City.
"I have asked to work hard (in training). For pre-season preparation you have to work hard and there is less than one week to be ready."
Tweet: Sanogo will be better than Giroud at his peak. However, that time has not come yet. OG is still the main man up front.
Arsenal's pre-season preparation also saw them take a squad to face New York Red Bulls in the United States, with most players who were involved on World Cup duty excused from making the trip.
Giroud feels there is an obvious gap in fitness levels between those players who have been back in training for a longer period but is backing Arsene Wenger's side to have a great season once everyone is up to scratch.
"I didn't got to New York, along with a lot of players, so we are at a different stage so it is hard to value our potential but when we are fit and all together we will do fantastic things," he said.
"We just have to work at our training and we have a fantastic test on Sunday, we will be ready I think because we want to win this first trophy."
Wenger is not concerned about Giroud's fitness and put his display on Sunday down to a lack of rest.
"Today at least he was not ready at all," Wenger said after the game.
"He had only three weeks rest, it was not an eternity and he had to come back quickly. But sometimes when you come back late you want to work hard and in a game you are not as sharp. "It's nothing about him. 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."
After the Wembley showdown against City, the Gunners get their Premier League campaign up and running at home to Crystal Palace before the first-leg of their Champions League qualifier.
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