At the time of the invasion it was seen by the Cubans as the ultimate failure for the United States. They acted out of a fear of Communism and because geographically Cuba could threaten the U.S.. The Cuban government/regime viewed the invasion as a way to consolidate their own power as Fidel Castro had said beforehand in a speech to the UN that the U.S. would try to invade and nobody took much notice. The 'win' against the stronger country and historically (neo)colonial power was a cause for great celebration. In Cuba the U.S. was seen as vast political other who had unfairly dominated their economy and politics for far too long so you can imagine how many Cubans felt. Middle class Cubans (predominantly white) would have seen the invasion as a failure to 'save them' from the 'evils' of a socialist society. This same class was made up of many who had either already left Cuba or who would leave after the invasion.

Hope that helps, forgive any bad formatting!