Neither of the two former winners attended the otherwise star-studded event at Royal Festival Hall.
But that didn't stop Modric - who also claimed the Golden Ball award as the player of the tournament in Russian Federation - from being voted as the best player for 2018.
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"Of course we can win our fourth straight [Champions League title], nobody believed we could win the third and here it is".
Modric and Ronaldo on a third successive Champions League in May before achieving something far more unexpected: captaining Croatia to its first World Cup final.
'First of all I would like to give congratulations to Mohamed and Cristiano (Ronaldo) for the great seasons they had'.
Modric has become the first player other than Messi or Ronaldo to claim the Federation Internationale de Football Association award since Ricardo Kaka lifted it in 2007.
Salah, who disappeared after the ceremony without speaking to any media, had said before the awards were announced that he was not pinning his hopes on victory, instead looking forward to the future.
The award was decided by a combination of votes from the captains of each worldwide team, coaches of each global team, selected members of the media and the fans.
Croatia captain Luka Modric was ecstatic after winning FIFA Best Men's Player Award on Monday but kept his emotions in check and dedicated the trophy to everyone who loves football.
The 32-year-old Marta, whose Orlando Pride team reached the the US National Women's Soccer League (NWSL) playoff semi-finals, had won the previous FIFA Women's Player of the Year award five times, most recently in 2010.
Interestingly Thibaut Courtois - who changed tack and thanked both his current club Real Madrid and former team Chelsea, from whom he left under a slightly dark cloud - won Best Goalkeeper, but was excluded from the overall "dream team".
"The absence of Ronaldo and Messi?"