Lara's side have lost all three of their games in the Super Eights stage with the 113 run-defeat to Sri Lanka following comprehensive losses to Australia and New Zealand and the destiny of the tournament hosts is no longer in their hands.
"There is an equation that allows us to get there but we have to depend on a lot of teams to get certain victories.
"We have got to regroup, we have one game in the next 18 days and we have a lot of time to regroup for the last three matches and we have got to remain upbeat and represent the Caribbean," Lara told a post-match news conference.
The hosts, winners of the first two World Cups in 1975 and 1979, had been hoping to become the first home country to win the event.
"I am an eternal optimist and I am going to focus on what is ahead. It takes a lot of good cricket from us and a lot of luck to get there.
"We have to ask the fans to come out and support us. It is a tough tournament but we have an outside chance and I'm going to be focusing on that," added the West Indies skipper.
'TOTALLY OUTCLASSED'
Sri Lanka set West Indies a target of 304 to reach but Lara's team never mounted a threatening challenge and ended up 190 all out.
While Lara accepted his side had been "totally outclassed" by Sri Lanka and had been "outplayed" in all three second-phase games so far, he rejected the suggestion that his top order batsmen were simply not good enough.
"They are capable. If you look at their stats they have played match-winning innings. It is just that it is a barren time for them at the moment," he said, adding that fatigue may have been a factor in his team's display on Sunday.
"We have played four games on sandy outfields in 10 days, it is tough. What is good is that we have a break now and we can come back refreshed and strong for the last three games," said Lara.
"It still boils down to us beating South Africa, Bangladesh and England to give ourselves any glimmer of hope and that is a job only we can do," he said.
"We are in a crisis situation, pertaining to cricket, we have got to dig ourselves out of that hole and we have been trying," he said before defending his side's approach to games.
"The performances have not been up to scratch but that is not to say we don't go out on the field at 9.30 in the morning thinking positive and thinking we can win," he said.
