Andre Breitenreiter's side went into the encounter at the Allianz Arena top on goal difference after collecting eight points from four games in their debut Bundesliga season.
Defending champions Bayern were among the other sides on eight points and had come under fire from some sections of the media for an unspectacular start to the campaign by the club's own high standards.
However, an easy triumph thanks to goals from Thomas Muller, Robert Lewandowski and a Mario Gotze double ensured Bayern moved top and Robben feels the win serves as a warning to rival clubs.
"It was very important for us to win and to set an example," the Dutch winger told reporters.
"We were just the better team. They had some problems in the beginning and we exploited
"We were quickly 2-0 up after taking the lead. Now we must go on."
Bayern went into the clash on the back of a disappointing 0-0 draw with struggling Hamburg last weekend and Gotze was pleased Bayern produced a good display on Tuesday.
He added: "We were well prepared and wanted to make up something from the last game.
"It was important that we got the three points, especially at home and we succeeded.
"We have played a relatively good match, so congratulations to the team."