The £8.5m centre half’s Croatia side needed to beat Mexico in their final Group A game in order to qualify for the knockout stages but they were defeated 3-1 on a disappointing night.
The Croatians struggled to create a single chance and Mexico were good value for their win.
Nearly all the major chances of the match were created by the South Americans.
Hector Herrera struck the bar after 16 minutes while Oribe Peralta produced an awful finish when played through on goal.
In the second half Vedrun Corluka headed a corner off the line before Mexico had a superb penalty appeal for handball controversially waved away.
Mexico took control of the game as Croatia faded still further and scored two goals in the space of three minutes to help them to the runners-up spot in the group to Brazil and a game against the Netherlands in the last 16.
Rafael Marquez, captaining his side in a record fourth World Cup, headed home the opener from a corner on 72 minutes before Andres Guardado added another three minutes later.
Javier Hernandez secured the result with Mexico’s third eight minutes from time.
Croatia netted a late consolation through Ivan Perisic before their misery was completed when Ante Rebic picked up a straight red card for a horrible challenge.
It left Lovren joining teammates Adam Lallana and Luke Shaw in being dumped out in the group stages.