The Windies were eliminated from the competition in England after tying with South Africa in a rain-affected final group game. Kieron Pollard's dismissal raised the Duckworth-Lewis par from 187 to the 190 the West Indies had already scored and the rain immediately returned, denying them victory.
A scheduled two-Test home series against Sri Lanka has been replaced by the one-day series also involving the trophy winners, and Gibson is pleased to have a swift chance of redemption. "I think we were starting to shape up to do well in that tournament. It's just to kick on from there," he said.
"It's to put away those little mistakes that we made in England. We felt we had a good opportunity to win that tournament and we want to win this one and prove ourselves right."
The hosts open the series against Sri Lanka on Friday and then face India on Sunday, both at Jamaica's Sabina Park, before the two touring sides meet at the same venue on Tuesday.
A second round-robin then takes place at Queen's Park Oval in Port of Spain, which will also host July 11's final. Sri Lanka reached the Champions Trophy semi-finals, where they were beaten by India, and captain Angelo Mathews hopes to build on that good run with a strong start.
"We played some really good cricket in the ICC Champions Trophy, beating England and Australia to reach the semi-final, and so the confidence is pretty high," he said.
"The West Indies are a strong team when it comes to the shorter format of the game. I think our main challenge is to try and adapt to the conditions as soon as possible. We are looking for a good start, so hopefully we can beat the West Indies and start on a winning note."
They will be without opening batsman Tillakaratne Dilshan, who suffered a calf injury in that semi-final loss, and Mathews continued: "It's unfortunate that Dilshan picked up an injury, but it is a good opportunity for our youngsters to try and prove themselves."
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- the West Indies