The Russian side needed to match Manchester City's result at Roma to guarantee a spot in the last 16, while victory would have taken them through in the event of a draw at the Stadio Olimpico.
However, CSKA failed to impose themselves on Bayern at the Allianz Arena, and succumbed to a 3-0 defeat which eliminates them from European competition for the season.
Thomas Muller's first-half penalty and late goals from Sebastian Rode and Mario Gotze helped the Bavarian side ease through with five victories from their six Group E fixtures.
While naturally delighted to win, Robben was quick to point out CSKA's curious apparent unwillingness to press on and look for a vital win.
"Moscow weren't at all positive, they pulled everyone back and waited to hit us on the break," he said.
"We had total control over the game.
"If we'd seen our moves through to the end a little better in the second half, we'd have scored a couple more goals. But it was fun.
"It was a tough group but all credit to the team because we’ve done well."
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