The transit hotel is nice and fairly reasonably priced. You can also stay at one of the many hotels within minutes of the airport that target transit customers. Check with the information desk after you get out of the secure area. Lots of options plus they can help you make reservations or at least call the hotel so their shuttle driver knows to pick you up. I usually do this for overnighters in ICN just because I get to wander around town and get some good local food. Just be prepared to deal with non-English speaking places.

If you really can't get a transit hotel room and don't want to leave the airport, you can head to the upper level near the transit hotel and just crash on one of the many recliners or cushioned benches. There are a few such areas above the duty free shops so just look out for the escalators/stairs. Lots of people do that. They even have free shower facilities available.

ICN is a really nice airport for transit so relax and enjoy.