PSG host relegation battling Le Havre on Saturday
"It hurts but we gave it our all this evening and it's grim going out in this way," Robben told Dutch television after the game.
The Netherlands went out as they lost 4-2 on penalties after a goalless draw over 120 minutes in Sao Paulo.
"Unbelievable. It's tough, but that's what sport is about," said Dutch defender Ron Vlaar, who missed the first penalty. "I wasn't nervous, I concentrated. It had to go in and it didn't."