The video featured Lovren mocking Spain and appearing to hint he deliberately stuck Spain's Sergio Ramos with his elbow.
Tin Jedvaj scored his second goal three minutes into stoppage time to earn Croatia a 3-2 victory and a first win in a competitive match since beating England in the World Cup semifinals.
Modric beat out Liverpool's Egyptian forward Mohamed Salah and Ronaldo, who along with Messi did not attend the glitzy awards ceremony in London.
The comment came after Modric was named as UEFA Best Player of the Year and earned a nomination for FIFA's 2018 Best Men's Player award.
The tournament is being organized by the Croatian Football Federation in cooperation with Slovenian Football Federation.
More than 100,000 people thronged the square to hail 'Vatreni' led by captain and World Cup Golden Ball winner Luka Modric.
FIFA World Cup 2018: 'Big brother' Luka Modric from a different planet, says Croatia midfielder Ivan Rakitic
Rakitic and Modric form one of the most formidable midfield pairings at the World Cup and after an impressive start, Croatia are being tipped to go far.
Twenty years ago, Croatia reached the last four, being denied a World Cup final spot only by a Lilian Thuram-inspired France.
Modric has been one of the stars of the World Cup so far, scoring in each of his opening two games as Croatia have stormed to the top of Group D.
Midfield maestros Luka Modric, Ivan Rakitic the FIFA World Cup's best, says Croatia defender Vedran Corluka
Corluka is hoping to follow in the footsteps of living 'legends' and recreate Croatia's historic run to the World Cup semi-finals 20 years ago.
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.