The striker was Swansea's top scorer with 14 goals last term, but manager Michael Laudrup's decision to push free-scoring midfielder Michu into a more attacking role has forced the former Watford man to settle for a place on the bench.
And loan signing Itay Shechter was preferred to Graham in the 2-1 win over Newcastle as injuries saw Michu restored to the middle of the park.
"I'm third choice at the minute, by the look of it," Graham told Wales Online.
"Itay came in and did ever so well, credit to him, he was unlucky not to score. Then Michu can also go up top so there's extra competition for the places up front.
"It's a challenge but I've held my hands up and said I was right to be dropped - I'm not going to hide from that. It's how you react.
"The gaffer has said he was happy with the way I reacted and I'm professional enough to understand the ins and outs of football."