Graham joined Martin O'Neill's side on deadline day for £5 million only days after being booed at the Stadium of Light in his final appearance for Swansea.
The hostility towards Graham goes back to comments he gave to a Newcastle United fanzine in which he said he would never play for the Black Cats.
"I’m not going to hide from it. The comments were made, they came out, whatever. As footballers there’s a lot worse comes about other people," he told the Daily Mail.
"Now it is about putting that to bed, coming in the door, 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.
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"It couldn’t have happened any worse for me. Swansea v Sunderland the day before deadline day! I wasn’t a Sunderland player, I knew I was going to get abuse. You get it everywhere you go.
"But I was expecting not to come on and I was going to be safe!"
Graham made his Sunderland debut against Reading and was pleased to receive a positive reaction from the travelling Sunderland support.
"But the reaction I’ve had since I signed and showed I wanted to be here has been totally different. The reception I got at the Madejski last week was unbelievable," he continued.
"I play in the ideal position to create a relationship with the fans. They will see my commitment on the park over the next few weeks. That will be the end of that story."