Giroud scored a stunning effort against Crystal Palace on New Year's Day, flicking out his left boot and sending the ball over goalkeeper Wayne Hennessey in off the crossbar.
Mkhitaryan scored in similarly astonishing fashion at home to Sunderland less than a week prior and his effort saw him claim Goal of the Month for December.
However, Giroud believes his was the pick of the pair.
"Actually, they were teasing me, saying that the Mkhitaryan one was better!" he said in a Q&A video with Sky's 'Soccer AM'.
"It's crazy that two similar goals were scored in one week. I don't know if I got inspired, it's destiny.
"He did very well as well, but I think mine is better! But to be serious it was funny in the dressing room, we were all surprised by what happened."
Giroud has scored seven goals in the Premier League this season as Arsenal sit fourth in the table, eight points adrift of leaders Chelsea.