Although born in Ipswich and having grown up supporting Ipswich Town, Pennock began his career with their fiercest rivals, Norwich City, where he progressed through the ranks to turn professional in 1989. He was only to manage one appearance for the Canaries' first team, however, and in 1992 he was allowed to move to AFC Bournemouth for a fee of £30,000. He was a regular for the Cherries until he suffered a knee injury in December 1995 and was unable to regain his place in the team. In October 1996 his former Bournemouth manager, Tony Pulis signed him for Gillingham for £25,000.
Pennock spent over six years at Priestfield Stadium where he was a regular in the first team until a recurring knee injury took its toll. He developed a reputation as a practical joker whilst with Gillingham - during one pre-season friendly he switched on the pitch sprinkler system during the match. He also scored a memorable own goal against Wigan Athletic in 2000 which spawned a recurring terrace chant of "He only scores own goals". Such was his affinity with the fans that he even acquired his own fan club. On the pitch, he was named captain for the play-off final in 2000 which saw the Gills promoted to the Football League First Division for the first time in their history.
In January 2006 he was involved in a dispute with Gillingham chairman Paul Scally over a testimonial match which Pennock alleged he was promised as part of his final contract at Gillingham but which never materialised.
In January 2005 Pennock was appointed manager of Welling United of the Conference South and by the end of the season had guided them to their best league position for six years. He left Welling at the end of the 2006-07 season to take up a coaching position at Stoke City, under his former Gillingham manager, Tony Pulis. He left Stoke at the end of the 2012–13 season.