Rakitic and Iniesta won three La Liga titles, four Copa del Rey trophies and a Champions League together between 2015 and 2018, and the Croatian said he was stunned that Fernando Hierro overlooked the World Cup winner as Spain went up against Russia in the round of 16.
Iniesta replaced David Silva after 67 minutes of the game, which ended in a penalty shoot-out victory for the hosts after a 1-1 extra-time draw.
As Croatia prepared to face Russia in Saturday's quarter-final, Rakitic shared his reaction to learning Iniesta was on the substitute's bench.
"At that moment, I felt that I did not understand anything about football," Rakitic told El Pais.
"I thought I was playing another sport, to see the best player - maybe in history in his position - on the bench hurt a lot."
Turning to his rival at club level but team-mate on the international stage, Rakitic described Croatia captain Luka Modric as "a leader" and admitted he loathes playing against the Real Madrid star.
Modric has scored two of Croatia's eight goals en route to the quarter-final, and Rakitic spoke of the 32-year-old's importance in Spanish football.
"It's a pride for all Croats to have a player like Luka, but I do not like to see him in Madrid," said Rakitic.
"He improves anyone around him, it shows when he is not there, Madrid is a different team without Luka."