The Sox finished the season 63-99, tied for the fourth-most losses in team history. They dropped 23 of their final 30 games.
Quintana gave up another two-run homer in the seventh to Brett Hayes for a 4-1 Royals lead. Quintana closed out the inning to reach 200 innings on the season for the first time in his career.
Chen went 6 2/3 innings, gave up four hits and one earned run, struck out foru and walked three.
Quintana gave up four earned runs on six hits over seven innings. He struck out four and walked two.
The Sox already began the restructuring process Saturday night, whey they fired hitting coach Jeff Manto.