Wright made his debut against Derby County on 29 September, keeping a clean sheet in a 2–0 win at Pride Park which put his team on the summit of the table. On his UEFA Champions League debut against Panathinaikos he saved an Angelos Basinas penalty to help his side win 2–1. Despite an injury to Seaman which gave him an extended run in the team, he did not capitalise on the opportunity, punching the ball into his own net in a 4–2 home defeat to Charlton Athletic on 4 November when trying to clear from Paul Konchesky, and then two weeks later he was at fault for Gus Poyet's injury time equaliser in the North London Derby against Tottenham Hotspur. Four days later, he was substituted at half time with injury in a UEFA Champions League match away to Deportivo de La Coruña, being replaced by youth goalkeeper Stuart Taylor in the 2–0 defeat. He slipped to third choice behind Taylor and played mostly FA Cup matches for the remainder of the season, up to and including the semi-final against Middlesbrough, although Seaman replaced him for the final, which Arsenal won 2–0 against Chelsea. He made his last Arsenal appearance on the final day of the 2001–02 season, a 4–3 victory over Everton. He ended the season with 12 league appearances, meaning that he had earned a winners' medal; he was substituted for Stuart Taylor, so that Taylor also had 12 appearances and earned a medal. Wright made 22 appearances for Arsenal in total.