Robben gave the Dutch a lead they never looked like relinquishing after 18 minutes of the last-16 tie when he jinked inside from the right and drilled home a superb left-footed strike from 25 yards.
The winger continued to torment the Slovakian defence throughout the match as Weiss's side failed to scale the heights of their exhilarating 3-2 win over champions Italy in the group stages.
"We had three huge chances when the result was 1-0 and had Robert Vittek managed to take his chances, it could have been a different story. But in the end, if you make mistakes you are punished," said Weiss.
Vittek scores consolation from the spot
Striker Vittek eventually hit the target when he converted a penalty with the last kick of the game to take his World Cup goals tally to four.
Slovakian boss Weiss also took heart from his side's achievement of reaching the last 16 in their first World Cup as an independent nation.
"We played with heart and courage and we are proud that we made it to the second round, but the better team went through - Holland were great opponents," stated Weiss.
"I am happy with my players, although I believe they could have played much better but the penalty at the end will make us feel better during our flight back home."
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