The erstwhile giants of the game, who won the first two 50-over World Cups and dominated the game largely because of their dreaded pace attack, have gone without a major title since winning the 2004 ICC Champions Trophy.
Having arrived in Sri Lanka with a team teeming with hard-hitting batsmen, Sammy wants to win the Twenty20 World Cup and give the fans back home something to cheer about.
"When we left the Caribbean that was the most important thing in our minds, winning this tournament for our fans," Sammy said.
"The last decade has been tough for us. We last won a silverware in 2004.
"It is a good opportunity for us to do that here. We've been playing well as a team and we have to take it one game at a time," said the jovial all-rounder.
West Indies beat England by 15 runs in their first Super Eight stage match on Thursday and a victory against hosts Sri Lanka on Saturday would assure them a semi-final berth.
Leading a team containing mercurial players such as Chris Gayle, Sammy said his brand of captaincy has resulted in a relaxed dressing room.
"I just keep everybody cool. We have a lot of cool guys so when you're out there, you need to have someone in charge.
"When I'm out there I try to get all the senior players involved in decision making so everyone feels a part of the team.
"That's the important thing for us and it's easy to do that because my character allows me to involve everyone," said the 28-year-old player, first from St Lucia to lead West Indies.
Dwelling on Saturday's match, Sammy sounded wary of the senior Sri Lankan players such as captain Mahela Jayawardene, Kumar Sangakkara and Tillakaratne Dilshan.
"The senior players always turn up for them and they have a good mix in the squad," said Sammy.
"You just can't count them out at home. Playing them is a big challenge but it's one we're ready for," he said.
His Sri Lankan counterpart Jayawardene was relieved after narrowly beating New Zealand via Super Over in Thursday's thriller.
"When you are leading a team in a pressure situation and a crunch game like this, points on the board are very important," said Jayawardene.
"The first Super Eights game, a big occasion, we didn't get the momentum in the first few overs. After that we won a game, so that's good.
"At the end of the day what mattered was that you handled the big moments a bit better than the other team. We can build on this," he added.