The midfielder, who signed for Arsenal two years ago, has lost a regular spot in the North London side.
"Arshavin's been a poor buy, his enthusiasm doesn't seem to be there," Graham told talkSPORT.
"Last night [against Marseille], and in the past, he's looked like he doesn't want to be there. When he pulls that shirt on he's not been good enough for me."
Arsenal claimed a late victory against Marseille in the Champions League last night.