The loss meant that Croatia's interest in the competition was over with Brazil and Mexico advancing from Group A into the last 16.
"Goodbye dreams!," commented the state-run HRT television speaker after Guardado scored for a 2-0 lead for Mexico in the 75th minute.
Cafe terraces across Croatia as well as main squares in many towns were packed with people watching live broadcast of the match and hoping that their squad, known as the 'Fiery Ones' (Vatreni), would win to stay in the tournament.
"It was imperative that we won ... We tried everything but simply the opponent was better.
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"We gave our maximum and it was not possible to do more," the 42-year-old former Croatia captain concluded.
The clash had been dubbed as Croatia's "Match of the Decade" opening up the possibility of a first appearance in the World Cup last 16 since 1998.
"The stakes were high! At the start it was a tough game, but Mexico were better, more solid," admitted Ivan Joskovic, a 30-year-old electrician who watched the match along with thousands of other fans at Zagreb's main square.
His view was echoed by many other fans, many of whom were sporting Croatia's distinctive red and white squared shirts as they followed the match on a 52-square-meter screen above an improvised stage.
"Unfortunately, Mexico deserved to win," said 24-year-old student Dario Narkic.
"We fell apart and the Mexicans broke us! We should have played better notably in second half," his friend Vinko added.
"Disaster in Recife!" read the headline in the influential Jutarnji List daily online edition.
"A sad farewell of the Fiery Ones from Brazil! Mexico broke us in the second half" the paper commented.
"But Mexico were better and they deserved to celebrate with a high 3-1" the paper commented in its online edition.
Ever since the World Cup started on June 12, with Croatia's opening match against hosts Brazil, the small nation has been gripped by football fever.
Cafes installed new TV screens on terraces and redecorated their premises in the red and white chequerboard pattern.
Apart from live broadcasts in the main squares of big towns and cities, giant posters of the Croatian team stared out from shop windows, notably midfielder Luka Modric and striker Mario Manduzkic.