Pejic was born in Chesterton and joined the youth teams of Stoke City in 1977 where his older brother Mike had just spent ten years.
Of these, 412 were in league matches, for which he holds the club's Football League appearances record, where he also scored 14 goals, and puts him second in the all-time appearance list for the "Bulls", behind John Layton who played a total 549 times for the club during their non-league days.
He moved to Wrexham midway through the 1991–92 season, and went on to make over 100 league appearances for the "Red Dragons" helping the Welsh side to gain promotion in 1992–93.
Towards the end of his playing days he firstly completed his FA Diploma in the Treatment and Management of Injuries, before studying and gaining a Physiotherapy Degree from Salford University, later taking over first physio duties at Wrexham and then under the managership of John Toshack the Wales national football team senior physiotherapists position, being promoted from a similar position with the Under 21 team.
In November 2013 Pejic returned to Stoke City to work in the medical department at the club's academy.