Norwich reached the semi-final of the FA Cup in 1989 with Gunn in goal, but he missed the semi-final in 1992 through injury. What has been described as his—and Norwich's—greatest moment came in their upset victory over European giants Bayern Munich in the UEFA Cup in 1993. "The Independent" described the match as "the pinnacle of Norwich City's history". Gunn made several saves that kept the Canaries in the match. He describes the save he made from Bayern striker Adolfo Valencia as the finest of his career; it has also been described as "one of the most outstanding saves by a City goalkeeper". However, he was involved in an own-goal incident in an East Anglian derby match in the 1995–96 season, when a backpass from Robert Ullathorne bounced awkwardly off the pitch and over Gunn's attempted clearance kick.