Burgess began his career at Tranmere Rovers in 1981, and went on to make over 200 league appearances for the Wirral club in five years.
In 1986 he signed for Grimsby Town. In two years at Blundell Park he made 69 appearances.
He returned to the west coast in 1988 when he joined Sam Ellis' Blackpool. He made just over 100 appearances for the Seasiders in five years, and was a member of the team that won the Fourth Division play-off final at Wembley in May 1992. This was after sitting out the entire 1990-91 season through injury.
During the following season he was loaned out to Carlisle United for a month, and made the move permanent later that season.
He spent a year with the Cumbrians, making 40 appearances and scoring one goal.
Another loan spell followed, this time at Hartlepool United, before moves to Northwich Victoria and Bamber Bridge, with whom he finished his career.