Atkinson, 21, scored on his league debut in the 2-2 draw at Wigan before making his first league start at home in the goalless draw with Liverpool on the final day.
Fellow youngsters Tom Cairney and Mark Cullen broke into the first-team squad last term while Nicky Featherstone and Jamie Devitt are back at the KC Stadium after loan spells in League Two.
With a number of high-profile player departures expected to ease the club's financial problems, Atkinson believes the youngsters can
do themselves proud.
Atkinson told the Hull Daily Mail: "It's definitely a big chance for all the young lads next season. There's five or six of us who can stake a claim and there's still some big games next season. It could be a real big year for us all.
"I believe I can make it in the Championship but it'll be up to a new manager and how he sees it. I'll be hoping for a big chance."