Despite wrapping up the league title in record time last term, Bayern suffered a loss of form towards the end of campaign and were dumped out of the Champions League by Real Madrid at the semi-final stage.
However, Robben feels Bayern are in good shape heading into the new campaign.
"No-one needs to have any worries," he told the club's website. "Obviously, our opponents will be even more fired up this season, but we know what we can do and we have a coach with so much experience of this situation.
"I think it's good we start with strong opposition in the shape of Wolfsburg, Schalke and Stuttgart. Everyone will be thinking, 'Hey, here we go again.' We can't afford to be careless."
Robben was included in the final shortlist for the UEFA's Best Player in Europe award, alongside teammate Manuel Neuer and Ballon d'Or winner Cristiano Ronaldo.