The hosts have just two points from four games following their crushing 113-run defeat against Sri Lanka here on Sunday. They had already lost to defending champions Australia and New Zealand in their first two matches.
Their two points came after their win over fellow-qualifiers Ireland in a group match. They will now take on England, South Africa and Bangladesh in their remaining three matches.
"We've a lot of time to regroup and make sure we win the remaining matches. Let's hope it's not too late. Let's make sure we have a chance. We have got to stay upbeat as we are representing the Caribbean," said Lara.
The West Indies play South Africa in Greneda on April 10, followed by matches in Barbados against Bangladesh (April 19) and England (April 21).
"I am an optimist. We'll be hoping that some teams beat others, but it still boils down to us beating South Africa, Bangladesh and England to give us a glimmer of hope and that is the job we have to do."
The West Indies were let down by their batting as they could manage just 190 chasing a stiff 304-run target, with only Guyanese pair of Shivnarine Chanderpaul (76) and Ramesh Sarwan (44) offering resistance.
"There is a little bit of light at the end of the tunnel and we have got to go for that and be strong," said the West Indies captain.
"I know everyone is disappointed in the dressing-room at the moment and everyone is disappointed in the Caribbean."
Lara said he hoped the senior players would deliver in the remaining matches to sustain the team's hopes.
"I think the senior guys are understandably disappointed," he said.
"They understand the situation and we are in a crisis situation now. The guys know we have to dig ourseleves out of that hole and move on."
Lara conceded his team were outplayed by Sri Lanka, saying left-handed opener Sanath Jayasuriya played a big role with his century.
"They were brilliant and outclassed us. They ticked all the boxes right. They have still got Australia and other teams to play and we now need to focus on ourselves," he said.
"Sanath was exceptional. It was 50-2 and we were trying to put pressure on them, but he built the innings and set the tone. Credit must be given to him."
Jayasuriya cracked a 101-ball 115 for his 25th century with the help of four sixes and 10 fours to help his team post a challenging total.
The West Indies faltered in reply as they lost three wickets for 42 runs, including that of Lara.
"We found ourselves in trouble, losing three early wickets before the innings reached any stage," he said.
"It is very disappointing, but there is still a slight equation to allow us to get there (semi-finals) but it would depend a lot on other teams."