On Thursday, Three Lions manager Gareth Southgate confirmed the FA had wanted to select Hudson-Odoi for under-21 duty.
But the Chelsea forward — who has three senior England caps — does not want to be considered for Lee Carsley's squad as they take on Czech Republic and Georgia this month.
Sinclair told talkSPORT: "The only one I would say is bad is Hudson-Odoi – and I don't mean to pick him out.
"For me, I think that's quite arrogant. A big part of being a footballer and a big reason why you make it is staying humble.
"There's a lot of ups and downs. When you're flying, you're alright, when you're not doing so well, you've got people who have got your back.
"I think Hudson-Odoi saying that he's not playing for the Under-21s is poor."
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