The Colombia star struck the only goal of the game as the holders bowed out of the competition, and he was left aggrieved that they could not make their dominance tell
The holders were beaten 2-1 on aggregate by the Russian side, with Falcao's late strike ultimately no more than a consolation on a night where the Spaniards dominated proceedings.
The 27-year-old was disappointed that they were unable to convert their dominance into the scoreline they needed, as los Rojiblancos were left to rue their poor performance in the first leg.
"I'm disappointed with the outcome of the game," Falcao was quoted as saying by Marca. "We travelled to Moscow only for the win, despite conceding the second goal [in the first leg].
"We dominated all over the pitch for practically the entire match as we tried to overcome the goals we conceded at home. Unfortunately, we didn't manage it."
Rubin Kazan goes on to meet another Spanish side in the round of 16, after Levante secured progression following its 4-0 aggregate win over Olympiakos.