The Red and White Wizards can still make the top six promotion push, but the Blades would need to make up six goals in a game at Wolverhampton Wanderers and bank that Reading and West Ham United lose on Sunday. A tall order but still mathematically possible.
"That's what makes it so frustrating," said Quinn. "The fact that I definitely think if we went up we'd stay up.
"I don't know what Sunderland or whoever else gets there will do, good luck to them, but what I do know is that we have the character and the spirit not to come straight back down.
"I think we're as good as Sunderland and they've gone straight up. That's why it's hard to take but we'll turn that frustration into a positive by channelling it in the right way," he told the Sheffield Star.