Spurs have earned many plaudits in recent years, having finished in the Premier League's top four in the last three seasons, but they have now gone more than a decade since last picking up any silverware.
Adams, who skippered England on home soil at Euro '96, is concerned that the Tottenham contingent may let their teammates down.
"I'm really worried about these Tottenham players; I don't think they know how to win," he told The Sun. "They're very good players but at certain points in seasons and tournaments, you have to step up - there's a psyche players must have."
England face Tunisia in their opening World Cup fixture in eight days' time, before taking on Panama (June 24) and Belgium (June 28).