The Saints defender started at the heart of the Croatian defence with his side realistically needing a win to qualify from Group A.
After a goalless first hour at Arena Pernambuco in Recife, Mexico struck three times in ten minutes to leave Lovren and his teammates shellshocked.
Rafael Márquez opened the scoring on 72 minutes, with Andrés Guardado making it 2-0 three minutes later.
Manchester United’s Javier Hernández made it three on 82 minutes, before Ivan Perišić pulled one back for Croatia five minutes later. However, any slim hopes of a comeback were killed off when Ante Rebić was shown a straight red card soon afterwards.
Croatia finish third in Group A with three points from as many games. Hosts Brazil win the group on goal difference ahead of Mexico, while pointless Cameroon foot the table.