Modric was awarded the Golden Ball as the tournament's best player, and Rakitic shared an image of the two together with the prize on his Instagram account after the 4-2 loss in Moscow.
"Brother Luka Modric, you do not know how proud I am!" said Rakitic.
"All deserved, we celebrate with our family and all Croats!
"Nothing more beautiful than to be Croatia."
While Modric starred for his country at Russia 2018, his personal prize offers little consolation on the back of a collective stumble at the final hurdle.
It may be that he has graced football's grandest international stage for the last time, with a 'Golden Generation' of talent set to be broken up.
Modric and Rakitic do, however, still have plenty to be excited about at club level as they seek to put World Cup disappointment behind them and hit the ground running in 2018-19.