World Cup chief executive Chris Dehring said the local committees in the Caribbean will have to be resolute if the hosts, who have lost all three of their Super Eights matches, fail to make the semi-finals.
That would have a further diastrous effect on crowd figures which been poor throughout the competition with many locals complaining they have been priced out of the stadiums.
Other fans are furious over expensive park-and-ride schemes, fussy security and the refusal to allow spectators right of re-entry into the grounds.
"It (a West Indies exit) would be devastating for all the hearts of the Caribbean but we can still put on a good tournament," Dehring told the BBC's Test Match Special.
"We can show we can appreciate cricket and we'll have to show some character."
Dehring said the three first round matches in Kingston, which featured the hosts had been sell-out affairs, but many ticket-holders had not turned up to the matches.
"Tickets get into the hands of people who just can't attend, for whatever reason," he said.
"I think we can be very proud in the Caribbean about what has taken place so far. There's a still a month of the World Cup to go. We are still focused on running this event professionally. Let history be our judge."
In Bridgetown, where the final will be staged on April 28, the local committee are already bracing themselves for an eerily-empty Kensington Oval on April 15 when Bangladesh face Ireland in the Super Eights.
That had been the date when it was expected India would lock horns with Pakistan in one of the World Cup's marquee match-ups.
The Barbados government has even set up an emergency task force to try and salvage the situation.
Barbados minister of tourism Noel Lynch told The Nation newspaper that the task force had been created for a number of reasons including the elimination of India and Pakistan, "which nobody could have predicted", the poor performance of the West Indies team, over-priced tickets, and the removal of "things like drinks and music" from games.
Many fans were left feeling "this event is simply not a Caribbean event", said Lynch.
He added that while hotel bookings were still running at 68-70 per cent, there was weakness at the luxury end. Up to the elimination of India, 80 per cent of cabins on a cruise ship hired for the duration had been booked.
Now, said Lynch, bookings on the ship were around 40 per cent.
Barbados is trying to entice fans from Ireland with a new marketing drive while Sri Lankan and Bangladeshi communities in Florida are also being targeted.
Lynch admitted that one major challenge in the salvage effort was to try and get back the large number of tickets which were sold in India.
"The window is short, but we are working as much as we can," he said.