Switzerland remained winless in this year's Nations League and they were relegated to the second tier league B after Serbia held them to a 1-1 draw on Friday, with Zeki Amdouni's opener cancelled out by Aleksa Terzic's late strike.
The Swiss will finish bottom of group A4 with just two points from five matches.
Serbia kept their hopes of advancing to the next round alive, sitting third on five points, two shy of Denmark, who lost 2-1 at home to leaders Spain.
After missing several chances to open the scoring, Amdouni curled in a fine half-volley in the 78th minute to hand Switzerland the lead before Terzic equalised following a counter-attack 10 minutes later.
The visitors had squandered a golden chance to take the lead early in the second half as leading scorer Aleksandar Mitrovic's penalty kick was saved by Swiss goalkeeper Gregor Kobel.
Serbia keeper Djordje Petrovic was also crucial in denying Switzerland the lead with key saves from attempts by Amdouni and Edimilson Fernandes.
Switzerland will close the group stage visiting Spain on Monday, while Serbia host Denmark.