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."
"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."
