Gayle managed just five runs in the World Twenty20 semi-final against India this afternoon, but last-minute injury replacement Lendl Simmons (83*), along with Johnson Charles (52) and Andre Russell (43*), helped the Windies to a shock victory over the tournament hosts.
They will now face England in the final on Sunday, and Sammy warned that are "15 match-winners" in the West Indies ranks.
"We said it even before the tournament started: everybody said Chris is under pressure, but I said then that yes, Chris is our best player but we have 15 match-winners in this squad. Games are won when players take responsibility, and Charles, Simmons and Russell took that responsibility against a very good Indian team," he told Sky Sports News.
"Look, it's a big step today. We came here on a mission, we were inspired by the Under-19s boys earlier this year, and the ladies did brilliantly to win this afternoon, and now we have two West Indian teams in the finals and I know that means a lot to the Caribbean people.
"Especially the men's side have been going through a lot. We all know what happened just before the tournament, and we still feel it's this West Indies team and this coaching staff versus everybody else."
West Indies have already beaten England in this year's World T20, with Gayle smashing 100 off just 48 balls on that occasion.