Bob McNab established himself at left-back in the 1967–68 season, and so Storey was moved over to right-back. Despite being a full-back he was sometimes given the job of marking a dangerous and creative opposition player closely, and though he was never ordered to use rough play he was on these occasions told "you know what to do, Peter". He was sent off for the first time in his career, along with Frank McLintock, in a 1–0 defeat to Burnley at Turf Moor in December 1967; despite his tough tackling he was actually dismissed for bad language. Arsenal finished the season in ninth place, but advanced past Coventry City, Reading, Blackburn Rovers, Burnley and Huddersfield Town to face Leeds United in the final of the League Cup at Wembley. Leeds won the game through a Terry Cooper volley on 20 minutes, and Arsenal barely created any chances in the game.