Carriço missed the first part of the 2015–16 season due to a tendon injury, but was still able to contribute 25 appearances across all competitions, scoring in a 1–1 away draw against RC Celta de Vigo. He also started in both of the team's finals: he helped them to a third consecutive Europa League title by defeating Liverpool 3–1 in the final in Basel, making a goal-line clearance from Daniel Sturridge's header after ten minutes and subsequently dedicating the victory to Antonio Puerta, a Sevilla player who died in 2007. On 22 May 2016, in the last minute of extra time of the final of the Copa del Rey against FC Barcelona, he was sent off for two bookable offenses in less than 30 seconds, first for tackling Lionel Messi then for calling referee Carlos del Cerro Grande a "faggot" in an eventual 2–0 loss, receiving a four-match ban the following day for his actions.