Despite a 2-1 victory for Madrid on the night, the Spaniards lost 3-1 on penalties after the teams were tied 3-3 on aggregate.
Mourinho believes that his side were drained from Saturday's El Clasico win over Barcelona, while Bayern reaped the rewards of resting their key players against Werder Bremen.
"The lads were fantastic, with an incredible mentality against a great team, against a team that last weekend were on holiday," he told reporters.
"We were maybe lacking a bit of freshness.
"It was a great, enormous game. We lost, we are sad and they are happy but that's football."
Munich will now face Chelsea in the final at the Allianz Arena on Saturday, May 19.