Weiss said the better team had gone through to the quarter-finals but that he was proud of his players for their performance on their debut in the tournament in which they sent home holders Italy with a 3-2 group stage victory last week.
"No coach can be happy if he loses if he has three high quality chances," Weiss told a news conference, referring to two excellent chances for Robert Vittek and one for Miroslav Stoch while they were still only one goal down.
"If we had managed to make goals out of these opportunities it would have looked different but then it changed to 2-0.
"When it was still 1-0, I told my players that it is not bad yet but they got a little bit nervous so we got punished."
Midfielder Stoch said the players could not be too upset by the result.
"The Dutch played really good football and that is why I think 2-1 against such a team was a good result for us, although it could have been much better," he told reporters.
Weiss added that the referee, who gave little Slovakia's way, had not helped his team's cause.
"It happens at the World Cup that the weakest link is often the referee and I would say it in this match it was again the referee, he just invented a foul for (Martin) Skrtel and it was a decision against us," he said.
"I am very proud of the players, I'm very proud they showed what they are capable of although they could have played a little bit better."
He said Vittek's last-minute penalty, which made the striker the country's all time top scorer with 23 goals and also the tournament's joint top scorer with Argentina's Gonzalo Higuain on four, had brought them some comfort.
"The penalty at the end will make us feel better during our flight back home," said Weiss. "The better football team has advanced."
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