萨维奇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. 萨维奇在歐羅巴聯賽上陣4次 and two more in qualifying as Fiorentina made the last 16 of the competition, being beaten 2-1 on aggregate by rivals 尤文图斯。He also played both matches in the 義大利盃 semi-final win over 乌迪内斯 and in the 決賽，where his side lost 3–1 to Napoli.