Late goals from Leroy Fer and Memphis Depay, who toe-poked home Robben's cross, downed Chile 2-0 in Sao Paulo as the Netherlands finished top of Group B.
The Netherlands also thrashed 2010 champions Spain 5-1 and overcame Australia 3-2 to raise hopes they could finally go all the way and win their first World Cup.
"We have to take time to enjoy this fantastic result but it shouldn't end here," said Robben, who nearly scored one of the goals of the tournament after an electrifying run from deep.
"We have to change our mindset and look ahead because we really want to move forward."
Coach Louis van Gaal was guarded over their chances of reaching a fourth World Cup final, citing uncontrollable factors like the debatable penalties they conceded against Spain and Australia.
"We'll have to wait and see,” said Van Gaal. “I think it depends on so many factors and a team doesn't always control all these elements.”
The Manchester United-bound coach took journalists to task as he bristled at suggestions that he wasn't playing attacking football at the World Cup.
"Could you give me a definition of attacking football? That's my question to you," said Van Gaal to one journalist.
"I'm asking you, if you have such a clever question... If you're going to ask me questions, I'm going to ask you questions."
Opposing coach Jorge Sampaoli had also criticised the Dutch tactics, saying, "We wanted to play but the Netherlands were just closing down.”
Van Gaal refused to comment, but he did say that his strategies were simply designed to win.
"It's all about winning so I use the system I think will let me win... that's what I think football is.”
Villa's tearful end to Spain career
David Villa extended his record goalscoring run at the World Cup on Monday and broke down in tears as he left the field as a Spain player for the final time.
Despite crashing out of the tournament, the world and European champions ended their World Cup campaign with a 3-0 victory over Australia 3-0. Villa registered his 59th international goal in his 97th and final appearance just before half-time.
However, the country's all-time leading goalscorer was surprisingly replaced by Vicente del Bosque just before the hour mark. Despite being consoled by teammates, Villa cut a dejected figure as his stellar international career came to an end.
"I have always had a lot of love for the national team and it has always been what I dreamed about," said the 32-year-old.
"I would play until I am 55 but that is impossible and I have to be realistic."
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