Ante Cacic's men went down to a 117th-minute goal from Ricardo Quaresma at UEFA EURO 2016 in a poor encounter, in which Croatia had its chances, in Lens on Sunday (AEST).
Ivan Perisic had hit the post with a header before Portugal broke and Quaresma nodded in after Danijel Subasic did brilliantly to keep out a Cristiano Ronaldo effort.
An unhappy Rakitic was in disbelief after his side's exit, saying: "They don't have a clue how they scored. If you ask them now how they scored, they probably wouldn't know.
"They say football is the best game in the world... but sometimes it is the dumbest thing in the world. That was tonight, because it is impossible that the better team has to go home.
"I don't know why things always break on our backs. Where is justice? Why is it always avoiding us?
"We played great the whole tournament, I can't believe we have to go home."
Fellow midfielder Luka Modric felt Portugal was fortunate, with Fernando Santos' men having sat deep – like Croatia – for much of the contest.
But the Real Madrid man, believes there is still time for his generation to have success at a major tournament.
"We all agreed the better team has to go home. We played good the whole tournament and didn't deserve to be out.
"We dominated, had the ball, created chances and they scored and won from some lucky counter-attack.
"Last chance of this generation? There will be time for deeper analysis, it is hard to talk about that... but no, it was not the last chance."