Savić continued to be a mainstay in the Fiorentina defence in the 2013–14 season, making 31 appearances in the league as Fiorentina again finished in fourth place. Savić made four appearances in the Europa League proper and two more in qualifying as Fiorentina made the last 16 of the competition, being beaten 2–1 on aggregate by rivals Juventus. He also played both matches in the Coppa Italia semi-final win over Udinese and in the final, where his side lost 3–1 to Napoli.