The Black Cats are winless in five Premier League matches and four points adrift of safety ahead of their meeting with the Hammers at the Stadium of Light.
Quinn, a former player, manager and chairman of the Wearside outfit, applauded their performance in defeat to Liverpool in midweek, but has stressed that only results are important at this stage of the season.
"It was another heroic performance from Sunderland but there was nothing at the end of it," he told Sky Sports News. "That's got to stop now - it's all about winning games, not letting their fans down again
"It's a huge game for them on Monday night; they've had this opportunity several times to win games at home after performances like this away from home.
"It's now about getting together as a group and saying to themselves it's now or never - we have to beat West Ham United and we've got to keep this club up."
Quinn scored 74 goals in 224 games for Sunderland between 1996 and 2002.