West Bromwich Albion striker Salomon Rondon tapped in the only goal as Venezuela reached the quarter-finals.
The defeat was the second in as many group games for Uruguay, with Mexico's 2-0 victory over Jamaica in Pasadena confirming their exit.
"We didn't play like a team that needed to get a good result," said Uruguay coach Oscar Tabarez.
Striker Luis Suarez, who injured a hamstring in Barcelona's Copa del Rey final win over Sevilla last month, did not feature for the second successive game for Uruguay, who top their World Cup qualifying group and are the most successful team in Copa America history.
"The player is not fit to play," said Tabarez. "I will not select a player who is not 100%. Was he angry? I am not aware. He told me nothing."
Venezuela, meanwhile, secured successive wins in the tournament for the first time.
Rondon became the first Venezuela player to score in three Copa Americas as he rolled home the 36th-minute winner when a long-range shot from Alejandro Guerra came back off the crossbar.
Mexico's victory was their 10th in succession since Juan Carlos Osorio took over as coach last year, with former Manchester United striker Javier Hernandez heading their opening goal.
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Fifteen-time champions Uruguay were knocked out of the Copa America as they lost 1-0 to Venezuela in Philadelphia.