The South Americans were beaten in the last 16 on Saturday night with a 2-0 defeat to Colombia.
While admitting that he is sad to be leaving the tournament, Cavani wants the Uruguayans to take pride in reaching the second round.
"We're clearly sad to have been knocked out. Losing hurts," the striker told FIFA.com. "Even so, we can still be proud and safe in the knowledge we gave it our best shot.
"It shouldn't be forgotten that during the tough times that followed the defeat to Costa Rica, the team proved there was life in it yet. We rose to the challenge."
Cavani leaves the World Cup having scored one goal in four matches.