The third-seeded Tigers fell 4-2 to the second-seeded Seminoles, who will play in the round of 32 vs. host Ole Miss, a 4-0 winner over Belmont earlier on Saturday.
Auburn's victories came at number one and number two singles while FSU won the doubles point plus the four, five and six singles matches.
At number one, junior Alex Schweizer took a 6-4, 7-5 victory over Ytai Abougzir while junior Robbert Lathowers was a 7-6, 3-6, 6-4 winner at two singles vs. Jonathas Sucupira.
At three singles, senior Nick Lane's match was stopped when FSU clinched the match with a win at six singles. Lane lost his first set 4-6 to Sam Chang, but rallied for a 6-3 second set win and trailed 5-4 in the third set.
At four singles, FSU's Macieck Kykut took a 6-4, 6-1 victory over freshman Milan Krnjetin.
Chris Westerhof was a 6-2, 6-1 winner over freshman Lukas Marsoun at five singles and Chris Cloer was a 6-4, 4-6, 6-4 winner at six singles over sophomore Pawel Dilaj.
In the doubles, Schweizer and Lane won 8-3 at the two spot, but Lathowers-Marsoun lost 8-5 at one to Abougzir-Westerhof and Dilaj and sophomore Terence Nugent of Auburn fell 9-7 at three to Bailey-Sykut of FSU.
Auburn ends its season with a 14-11 record. FSU improed to 18-11.