West Indies beat Australia by 74 runs in a lop-sided semi-final on Friday to set up a title clash with the hosts, who defeated Pakistan to reach the final.
"We needed our A-game to beat Australia and we have to touch better to beat Sri Lanka. We believe we can do that," Sammy said.
"Obviously, they know their conditions well. I just hope we get a very good cricket wicket, where batsmen could enjoy playing their strokes and the bowlers have something for them as well."
Sammy was hopeful that Chris Gayle, who smashed an unbeaten 41-ball 75 against Australia in the semi-final, would come to the party one more time.
"Once he is going, it's good for the team. We have the resources in the batting line-up too," Sammy said.
"Tomorrow is about every single person doing what they've been asked to do."
Sammy said West Indies would rather focus on their own strengths than worry about Sri Lanka's advantages on Sunday.
"Whatever we get, we just go out and execute the game plans. We're not focusing on them but we're going to put more emphasis on us," Sammy said.
"The crowd will be behind Sri Lanka but the belief in the dressing room is that we've done what we had to do to get to the final. Once we get there, probably we have to bring our A-plus game."
West Indies last won a major international title in 2004 when they won the Champions Trophy and Sammy was confident his team can end the long wait on Sunday.
"Winning will be massive. Over a decade, our fans are praying for bit of success," Sammy said, adding that the team's morale has been boosted by text messages from former World Cup-winning captain Clive Lloyd.
"I think work stopped yesterday (Friday) for a few hours, back at home.
"Winning means everything to us as players as well as the coaching staff. It will give us a big boost. Hopefully we could do that tomorrow."