The 25-year-old Irishman was inconsolable following the Blades' 2-2 derby draw with Barnsley at Bramall Lane on Saturday as the point was not enough to prevent Micky Adams' side slipping into the third tier for the first time since 1989.
Quinn, who started his career at Bramall Lane in 2005, said: "I don't know where my future will be. We will just have to sit down and see what the club says, whether they want me or not, but right now I'm not even thinking about that, I'm just devastated for this club."
He added: "As you'd expect we're absolutely devastated. It's disappointing for everyone involved with the club.
"The way things have been over the last few years, we thought we were progressing so for this season to end like this is devastating.
"We will just have to sit down and assess the season and look at how everything went wrong. At the start of the season we were looking at promotion so for it to end like this is I never would have thought. It hurts me, I have been at this club for eight years now and I am gutted."
Source: PA
Source: PA