 In 1982–83, he played in every one of the matches of the Dons' 1983 European Cup Winners Cup campaign, scoring a goal in the 3–2 victory over FC Bayern Munich in the second leg of the quarter-finals and becoming one of the "Gothenburg Greats" who lifted the trophy after beating Real Madrid in the 1983 Final.The following season, Simpson was in the team that reached the semi-finals of the 1984 European Cup Winners Cup and he scored a goal when Aberdeen won the 1983 UEFA Super Cup.In 1985–86, he helped the team to the quarter-finals of the 1986 European Champions Cup.