Louis van Gaal's men were beaten 4-2 on penalties by Argentina in their last four clash at the Arena de Sao Paulo, after the match had finished 0-0 following extra-time.
Robben, who had a great chance late in normal time blocked by Javier Mascherano, could not hide his despair at missing out on a final against Germany, although he was still proud of his team.
The Bayern Munich attacker also encouraged the 2010 runners-up to focus on their third-place play-off against Brazil on Saturday, rather than another opportunity missed.
"I think we should change our mindset quickly," Robben told NOS.
"We've done amazingly well to come this far. 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 converted his penalty in the shootout, but Argentina goalkeeper Sergio Romero stopped efforts from Ron Vlaar and Wesley Sneijder as his team advanced.
