Sri Lanka won their second warm-up match against the West Indies with four wickets to spare at the R. Premadasa Stadium on Tuesday, following their 156-run victory over the Netherlands.
"It's good to have won both the warm-up matches," Sangakkara said at the post-match media conference.
"I think there is still a lot of work to be done, mainly in the first 15 overs. There were worries and they were not good enough for World Cup cricket."
Sangakkara is also unhappy about the fact that his team lost six wickets while chasing down West Indies target.
"I think we should have chased it down with one or two wickets less than we did, but I think mentally we are slightly better chasing under lights now probably than a few years ago."
West Indies captain Darren Sammy felt his team should have scored more runs after Gayle gave them a good start.
"We should have scored more runs than we did, because we were well placed after 15 overs and then got some key wickets when they chased, but we didn't finish it off, that's what we should do when we play the main tournament," he said.
The West Indies face a tough opening game in Group B, against South Africa in New Delhi on February 24 -- but Sammy believes his team is battle ready.
"We know what we need to do and whether it's the first match or the last in the group, we need to give it the best," said Sammy.
The 14-team World Cup starts with a clash between India and Bangladesh in Dhaka on Saturday.