Pejic started his career with Stoke City under the management of Tony Waddington. He became a very important player in Stoke's successful early 1970s side, helping the club win the League Cup in 1972. A left-back, he was renowned for being a tough player and was prone to being sent-off, and on one occasion was suspended for five matches. He broke his leg in February 1975, and in his absence City's genuine First Division title challenge fell away. He was sold to Everton for a £135,000 fee in February 1977, where he played three seasons before joining Aston Villa in 1979. He retired due to injury in 1980.