Australia moved 2-1 ahead early in the second half of the Group B match, after a dominant first-half display, and began to dream of claiming one of the upsets of the FIFA World Cup.
While the Netherlands responded to eventually triumph - having initially led 1-0 through Robben's first-half strike - their left-footed winger conceded Australia had put his team 'under pressure'.
"They played really aggressively. They played like it was their last chance," Robben said.
"We were a little bit under pressure but we gave the ball away too easily."
Robben, however, was pleased with how the Dutch fought back with goals from Robin van Persie and Memphis Depay securing their second victory of the World Cup, after their 5-1 thumping of Spain to open their campaign.
With Chile knocking off Spain 2-0 in the second Group B encounter on Wednesday, Robben and his team-mates have qualified for the round of 16.
"We made a big step today. We have maximum points," the 30-year-old said.
"Goal difference can make a difference, so the first game was like an extra point for us."
The Netherlands' goalkeeper Jasper Cillessen labelled the game at the Estadio Beira-Rio a 'tough' one but underlined that the crucial factor was that Louis van Gaal's men had won.
"Ultimately, you want to win and we did. That is the key," the 25-year-old told Algemeen Dagblad.
"It was a tough match. Australia played hard and well, we had a hard time with it."
Cillessen added that Van Gaal's side would need to improve if they are to be a threat in the knockout stages.
"We want to be better. We are pleased that we have gotten through (to the round of 16) but we still have a match (to go)," the goalkeeper said.
"Tomorrow we are going to analyse this match and then we will focus on Chile."
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