Following a goalless draw, the Dutch suffered a 4-2 defeat in the penalty shootout and missed out on a place in the final.
Although he was disappointed by the defeat, Robben believes that his country have enjoyed a successful tournament and he has been quick to pay tribute to his teammates.
"We've done amazingly well to come this far," he told NOS. "Of course right now I feel disappointment, but we've done our best.
"From the bottom of my heart I can truthfully say you can see how everyone was behind the team. I think we can all be very proud of these players."
Robben scored three goals for the Netherlands at this year's World Cup.