The World Cup finalists have just one point from their opening two games and need to beat Scotland on home soil at Hampden on Tuesday to maintain hope of a place in the last 16.
More than 100,000 people thronged the square to hail 'Vatreni' led by captain and World Cup Golden Ball winner Luka Modric.
With a population of around 4.5 million, Croatia became the smallest European nation to reach the World Cup final in the 88-year history of the competition.
Some Denmark fans in Moscow expressed their frustration by booing at the final whistle after the first 0-0 of the tournament on Tuesday.
Croatia were already through to the last 16 and coach Zlatko Dalic rested most of the side that thumped Argentina 3-0.
FIFA World Cup 2018: Argentina striker Lionel Messi was powerless against us, says Croatia coach Zlatko Dalic
Real Madrid's Luka Modric produced a masterful display in midfield -- capped with a magnificent goal -- and Dalic said that his captain and number 10 had outshone his opposite number.
The Croatia squad is led by international stars Luka Modric, Ivan Rakitic and Mario Mandzukic, but on Sunday it lost a warmup game, 2-0, to Brazil in Liverpool.
The Croatians made group stage exits in 2002, 2006 and 2014, but the defender is confident the present team would finally live up to expectations.
Croatia took a gamble when they appointed Zlatko Dalic as national coach last October but he repaid them handsomely by guiding them to the World Cup finals.
Croatia coach Zlatko Dalic said he was worried about the impact of the false testimony charges against captain Luka Modric.
Zlatko Dalic will continue coaching the Croatian football team after reaching an agreement with CFF President Suker.