Koprivec started his career at
Koper. In summer 2007, Koprivec joined
Cagliari, and played two matches in the
2007–08 Coppa Italia, both of which Cagliari won; however, he did not make any appearances in the league. In July 2008, Koprivec moved to
Udinese, and immediately joined them in pre-season training. He made his league debut for Udinese on 22 March 2009 against
Genoa. On 17 August 2009, Koprivec was loaned out to
Serie B side
Gallipoli. He made his debut four days later, in a 1–1 draw with
Ascoli. During the season, he played only eleven games with the club from
Salento due to an injury that hampered his settling into the first team. He returned to Udinese at the end of the season, and was then included into the first team as a second-choice goalkeeper behind fellow Slovenian
Samir Handanović. On 15 July 2015,
Anorthosis Famagusta announced that Koprivec signed a 2+1 year contract with the Cypriot club. In May 2017 it was announced that Koprivec would leave the club at the end of the season. On 10 September 2019, Koprivec signed for
Scottish Premiership club
Kilmarnock on a one-year contract. He was released by the club at the end of his contract. In August 2020, Koprivec returned to Slovenia after 13 years and signed with
Tabor Sežana of the
Slovenian PrvaLiga. ==International career==