International Cricket Council (ICC) match referee Crowe imposed the fines after Brian Lara's side was ruled two overs short of its target at the scheduled finish of the Sri Lanka innings at the National Stadium on Sunday, said an ICC statement.
Sri Lanka scored a healthy 303-5 in their stipulated 50 overs after a 45-minute delayed start due to rain. West Indies were bowled out for 190.
"In accordance with the ICC Code of Conduct over-rate penalties, players are fined five per cent of their match fees for every over their side fails to bowl in the allotted time, with the captain fined double that amount," said the ICC statement.
As such, Lara has been fined 20 per cent of his match fee while his players have each received 10 per cent fines.
West Indies have now suffered three defeats in as many matches in the Super Eights following their 103-run mauling by Australia and seven-wicket thrashing of New Zealand.
West Indies, champions of the first two World Cups in 1975 and 1979, now have to win all their remaining three matches to have any hope of sneaking into the last four.
Pakistan and India - both out of the World Cup after first round - were the first two sides to be fined for slow over rates in the tournament.