Brazil was on course to reach the final four when Neymar finished a flowing move in expert fashion as half-time in extra-time approached, but substitute Bruno Petkovic struck a deflected equaliser as Croatia forced spot kicks.
Rodrygo and Marquinhos were unsuccessful in the shootout – the former denied by the outstanding Dominik Livakovic – as Croatia advanced to the World Cup semi-finals for the third time.
Brazil has now been eliminated from each of their last six knockout ties in FIFA's top tournament against European teams, with the manner of its latest defeat leaving Casemiro struggling for words.
"All defeats are painful, especially when you have a goal, a dream, you have a four-year job for that moment. It's hard to find words in these moments," the midfielder said.
"It's about lifting your head, life that goes on. We are sad, everyone in the group did their best. We get upset, mainly because of the way it was. It was in our hands, it escaped there.
"It's a hard moment. Now it's about having peace of mind, life has to go on."
Casemiro will be 34 when the next World Cup begins but the Manchester United man is in no rush to make a decision on his international future.
"I'm 30. Of course, there are always kids, but I'm 30 years old. I'm living the best moment of my career and I'm very happy at the club I'm at," he said.
"I missed an opportunity, but we need to see, especially now that a new coach will come in.
"You need to have respect. It's a tough time to talk about it, but we don't have to think about it now. It's about having tranquillity and a cool head."
Brazil's 38-year-old captain Thiago Silva, meanwhile, knows he will not get another opportunity to lift the famous trophy.
"Unfortunately, as a player, I will not be able to lift this cup. Who knows later with another role," the veteran defender said. "It's difficult to have words at that moment.
"I have already gone through some decisions in my life, not only in the national team, but personally.
"When we lose something important, which we aim for, it hurts a lot. You have to try to lift your head and follow it up, there's no other alternative. I'm a guy who got up every time he fell."