Graham was expected to move on over the summer after being told he does not figure in Poyet's long-term blueprint, but no acceptable offer came in for the ex-Middlesbrough man.
"We have 21 fit players, plus the two goalkeepers," said Poyet. "That is with Sebber [Coates] out injured.
"Those 21 include Cabral, Danny and Harry [Mavrias].
"They are there, so I'm not going to tell him [Graham] I don't want him and make him go and train on the side.
"It's clear that we've got three other strikers and I'm playing one of them.
"For me, he's alright and he's training every day.
"He doesn't complain, he's a great lad and trains well. He's got certain characteristics that I like too.
"But I need to pick things for the whole game and sometimes, other players deserve to play."
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