Following his £5m move from Swansea City, the 27-year-old has not received the full backing from fans after a comment he made about the club in his time at Watford.
Speaking to a Watford fanzine, Graham claimed that he would follow Gateshead rather than Sunderland if his boyhood club, Newcastle, ceased to exist.
"The comments were made and they came out," The Independent quotes him as saying. "There's a lot worse comes out about other people.
"For me now it is about putting that to bed, showing how committed I am to the club. Score a few goals and I'm sure that will all be forgotten and we can move on.
"I'm not the first Newcastle fan to play for this football club, and people have come here and had successful times. I want to do as well as I can here. Fans have their opinions but the reaction I've had since I signed and showed I wanted to be here has been totally different."
Graham made 62 appearances for the Swans, scoring 21 goals.