The France international, who won three FA Cups while at the Emirates, swapped the Emirate for Stamford Bridge in an £18 million deal in January.
However, in an interview with Willam Gallas who played for Chelsea and Arsenal, 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 in Chelsea.
“For this year, I think the title is gone but next year we will hold great ambitions. ‘I still have this desire to win before stopping even if I still have good years in front of me.”