The tournament started badly for the Celeste, who suffered an ignominious 3-1 defeat to Costa Rica in their opening Group D game.
Oscar Tabarez’s men bounced back, however, with consecutive victories over fellow former World Cup winners Italy and England.
The gloss was taken off their progression from the group stage, however, by Luis Suarez’s latest biting incident.
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Shorn of their key attacking threat, Uruguay were impotent against Colombia in their last-16 clash and crashed out of the tournament following a 2-0 defeat.
Despite elimination, Cavani refuses to despair, however, and is keen to look to the future.
“This group of players have been working together for many years and have achieved wonderful and important things," Cavani was quoted as saying by FourFourTwo.
"It'll now depend on the coach [Oscar Tabarez] and the FA [to decide] on any changes that might be made.
"It's a fact that there are solid foundations, made up not only of great players but also great people.
"When you've got that, it's easier to keep building."
Uruguay’s vanquishers, Colombia, will now go on to face Brazil in the quarter-finals at the Estadio Castelao, Fortaleza on Friday July 4.