Shaw started his career at Crystal Palace, coming up through their youth system. He enjoyed a brief loan spell to Hull City before becoming a major part of the first team, playing in the 1990 FA Cup Final. Crystal Palace were a "yo-yo-club" at the time after a promising start to the 1990s, where they also finished third in the league a year after reaching the FA Cup final. They were relegated in 1993, promoted in 1994 and relegated again in 1995, with Shaw being established as a regular player by the time they were in this period of instability. They also reached a further two League Cup semi-finals and an FA Cup semi-final in the five seasons which followed their FA Cup final appearance.