Bayern looked the more threatening side for large spells of the encounter at the Allianz Arena and took the lead through full-back Joshua Kimmich.
However, Real, who remain on course for a third successive Champions League title, rallied back with goals from Marcelo and Marco Asensio - profiting from individual errors by the home side.
And Rodriguez, who's currently on a two-year loan deal from Los Blancos conceded the performance produced leaves his side with regret, having limited the LaLiga giants' attacking influence.
"I'm angry because we've played a good game," he told reporters, as quoted by Marca. "They've had two clear chances and took them, and we've not taken four or five of our chances.
"It's football, now we have to think about the Bernabeu."