Van Persie upped sticks for a £22million move to Old Trafford last week.
Giroud, 25, insisted to The Sun: "I am not here to replace Van Persie or to make people forget him.
"I am here to bring something different. I don't have the pretension of saying I will replace him because I have every respect for him as he had an enormous season last year.
"I wish him good luck for the future but I need to bring what I can bring without being pretentious to say I am here to replace him. That would be very bad.
"I feel ready. Absolutely ready to assume the responsibility and make people say 'yes, we have Olivier'. That's how it is. If I didn't think that I would never get my chance. If you sign for a big club it's to replace another striker who leaves or you come and sit on the bench and wait for some game-time or wait until a striker is less efficient, needs a breather or is injured.
"Unfortunately that's how it is football. Now I have a chance as Robin left. So I will get more time to play and I need to assume the responsibility. In fact, I must.
"Because that is my chance and I have to take it. The ball is in my court and the show must go on."