Stoke's League Cup success won them qualification into the UEFA Cup for the first time in the club's history in 1972–73, and Conroy scored Stoke's first goal in Europe on 13 September, a 3–1 victory over German side 1. FC Kaiserslautern at the Victoria Ground. However Kaiserslautern won the return leg 4–0 to eliminate Stoke at the First Round. Stoke went on to finish 15th in the league, with Conroy claiming five goals in 39 appearances. The club then finished fifth in the 1973–74 campaign, but Conroy missed much of the season with recurring cartilage problems and featured in just eleven games. He underwent surgery to remove more cartilage from his knees, and as a result lost some of his natural pace and strength, making him a less effective player for the remainder of his career.