The retired full-back insisted that securing a top-four finish in the Premier League alone this term will not be enough.
"When I played in the teams that I played in there, the goal was to win as many trophies in that season as possible," the Evening Standard quotes Winterburn as saying.
"Top four is an achievement but it's not success like winning a trophy. The top four gets you back into the Champions League which Arsenal want to do.
"Being a player at a big club, you are judged on what you win."
Arsenal, who have climbed to fifth place in the league following a botched start which included two defeats in their opening three games, take on Watford at Vicarage Road this weekend.