Crosbie played a great part in Birmingham's winning the Second Division championship in the 1920–21 season, playing in every game and creating numerous goals. The following season, he won his second and last cap for Scotland, in a 1–0 win against England at Villa Park, Birmingham. He formed an excellent understanding with Joe Bradford, Birmingham's leading scorer throughout the 1920s. He set up Bradford's goal in the 1931 FA Cup Final, but this was not enough to give his side victory.