Graham was jeered by some home fans when he came on as a substitute in Swansea's draw at the Stadium of Light on January 29, two days before completing his £5m move to the Black Cats.
The 27-year-old grew up supporting Sunderland's rivals Newcastle, but the animosity seemed to have disappeared when Graham made his debut for Martin O'Neill's men in last Saturday's defeat at Reading.
"The reception was great at Reading," Graham told the Sunderland Echo.
"Obviously the one on Tuesday night was expected for myself. That's part and parcel of football, I just got on with it. But it never once put me off in terms of wanting to move here.
"The contrast with the reception I got at the Madejski Stadium was brilliant. I had signed and everything was done, and to get that reception was really pleasing.
"I'm just looking forward to having a successful end of the season."