The Netherlands midfielder opened the scoring against Portugal but admitted that his side were not good enough to progress after surrendering their lead to fall to a third defeat
The Oranje were seen as one of the pre-tournament favourites but failed spectacularly to live up to that billing and now return home on the back of three successive defeats.
Van der Vaart looked to have set his side up for an unlikely quarter-final spot when he put them ahead with a fine early strike, but Portugal fought back through two Cristiano Ronaldo goals to leave the Dutch bottom of Group B.
"We were not good enough this tournament," Van der Vaart admitted to NOS. "It was just a very poor performance by us. That's why we didn't deserve to go through.
"You know it's going to be a tough match. After our goal they were the better team. We were very poor. It's very disappointing, especially for the Dutch fans.
"After the loss against Denmark, you know it's going to be difficult, because you have to face two teams. Now we have to start all over again."
Portugal move on to face the Czech Republic in the quarter-final, with group winners Germany meeting Greece.