Starting the evening placed fifth out of five teams in Group B, Venezuela needed to better Ecuador's result against defending champion Brazil against a Peru side whose place in the knockout stages already looked safe.
However, Jose Peseiro's Venezuela was beaten by Andre Carrillo's second-half strike while its rival for qualification held the tournament host to a draw to progress instead.
That meant an early end to a disappointing campaign for Venezuela that returned just two points from four group-stages fixtures.
An understandably tense start to proceedings featured few chances, with two Jefferson Savarino efforts from distance providing the closest glimpse of goal for either side.
The second of those in fact created a gilt-edged opportunity for Sergio Cordova, but the Venezuela forward somehow conspired to head wide when presented with an open goal after a Pedro Gallese save.
Peru grew into the game from there, with Gianluca Lapadula and Sergio Pena bringing saves out of Wuilker Farinez before the break.
And La Blanquirroja picked up where they left off after the restart, with Carrillo reacting quickest when the ball dropped from a corner to smash the ball into the roof of the net.
That goal meant Venezuela were heading for the exit, and even worse news from Goiania followed, with Ecuador equalising against Brazil to strengthen their own chances of progressing.
With Venezuela's situation looking desperate, Peseiro looked to his bench for inspiration, but his side struggled to create chances of note as they were held at arm's length for the remainder by deserving winners Peru.