Perica started his playing career in his home-country of Croatia with Zadar in 2012. He made his debut for the first team during the month of September 2012. In his first season, he scored 8 goals in 20 league matches, and 10 goals in all competitions.
After his arrival at Chelsea, the club immediately loaned Perica out to Dutch club NAC Breda. On his NAC Breda debut he scored his first goal in a 1–5 victory away to Roda JC, having come on as a substitute. A few weeks later he scored the winning goal for 2–1 against Heracles Almelo in his fourth appearance. On 16 February 2014, he was sent-off just 4 minutes after being substituted on in the match against Feyenoord. In August 2014, his loan deal was extended for the 2014–15 season. However, after the sacking of Breda's manager Nebojša Gudelj, his role was reduced to a bit-part player and he requested a move in search for more game time. On 22 January 2015, his loan with NAC Breda ended and Chelsea loaned him out to Udinese until June 2016.
Udinese
On 8 February 2015 against Napoli, Perica made his debut for Udinese, coming off the bench in the 78th minute for Bruno Fernandes. On 1 March 2015 against Cesena, Perica came off the bench in the 84th minute, but was unable to prevent Udinese from losing 1–0. On 4 April 2015, Perica made his first start for Udinese in a match against Genoa that ended in a 1–1 draw. On 17 May, Perica scored the opener against A.S. Roma, the match ended in a 1–2 loss for Udinese. On 3 June 2015, Udinese extended Perica's loan deal for one and a half years. On 20 December 2015, Perica scored his first goal of the 2015–16 Serie A campaign in a 1–0 away victory over Torino, therefore scoring the winning goal in the 41st minute. On 15 June 2016, Udinese activated a clause in Perica's contract, in which he would join the Italian side on a permanent basis.
On 18 July 2018, Perica was loaned to newly promoted Serie A club Frosinone. The loan is set to expire on 30 June 2019. In January, he was recalled from Udinese to join Kasımpaşa after falling down the pecking order.
Loan to Kasımpaşa
On 26 January 2019, Perica was loaned to Turkish side Kasımpaşa.
Perica started his international career with the Croatian under-21 team. He played with the team at the under-20 World Cup. He was the youngest player in the Croatian squad and scored in a win over New Zealand.
