Savić was named as head coach of the Serbian National team after Dejan Udovičić left the position in 2012. Under Savić's leadership, the national team won the 2020 and 2016 Olympic Games, the 2015 World Championship, three European Championships (2014, 2016 and 2018), and six World League titles (2013, 2014, 2015, 2016, 2017 and 2019). In little over twelve months, between August 2015 and August 2016, the Serbian National team won consecutively all four of the biggest titles in Water Polo – the 2015 World Championship, the 2016 European Championship, the 2016 World League, and the 2016 and 2020 Olympic Games – an unprecedented achievement.