The French striker signed for the north London club’s local rivals Chelsea FC last month as he left The Emirates following a five-year stint with the Gunners.
Giroud was deemed to be surplus to requirements at The Emirates as the striker looks to try and gain some regular game-time ahead of this summer’s World Cup in France.
The striker helped Arsenal win three FA Cups during his time with the north London side but he was unable to help the Gunners win the Premier League.
Indeed, the north London side have not lifted the top flight trophy since their famous unbeaten triumph in the 2003-04 campaign.
And the 31-year-old has admitted that not being able to win the Premier League with the Gunners is his main regret.
Speaking in an interview with SFR Sport, Giroud said: “A regret? I have one and it is not difficult to guess.
“I do not know if we can really call it a regret but I have a little taste of unfinished business because I really wanted to win the Premier League with Arsenal.
“It does not erase five and a half years like that but I repeated it often enough: it was my goal.
“After, it’s not over, I’m still in the Premier League, now I’m at Chelsea.”
Giroud will be hoping to help Chelsea FC break back into the top four this season after their 2-1 loss to Manchester United at Old Trafford left them in fifth place in the table.
Chelsea FC travel to Manchester City in the Premier League on Sunday.
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