The West Indies are on a woeful run of form, having not defeated a Test side in a one-day international since June 2009 and slipping to a dismal eighth in the rankings.
"We are aware that we have a lot to play for here," said Sammy, 27, ahead of the match at the Feroz Shah Kotla ground.
"If we play to our full potential and take it step by step, who knows what could happen? We just have to believe in our ability and go out and execute our plans. It does not matter if you are number one or number nine.
"You still have to go out and do what you have to in order to come out victorious."
Sammy was confident he had a team which was capable of giving the more favoured sides a run for their money in the tournament.
"If you look at our team combination, it is quite good. We have a lot of potential match-winners. If we can put all that together on the field for 100 overs, it will give us the result that we want.
"We have a quiet confidence in our team, the guys are well aware of what is at stake and we intend to show that once the action begins."
Sammy dismissed suggestions of ego clashes in a squad which features four former captains, three of whom can boast over 20,000 ODI runs between them.
"It is a good thing. The experience that these players bring to the side is helpful to me as a young captain. The younger players in the squad look up to them. So it's a plus for me to have these guys."
Sammy said his team realised the importance of winning a World Cup at a time when the game was struggling back home.
The West Indies won the first two World Cups in 1975 and 1979, becoming the undisputed kings of the one-day game, but have since struggled to make a mark on cricket's showpiece event.
"Fans back home want to see the West Indies go out there and play with pride and passion. They want us to show the same fight and passion that we had back in the eighties.
"If we can give our best out there, it will really make them happy."
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