The Ivory Coast midfielder put in a poor performance as Jerome Boateng's late strike against his former club earned the hosts a 1-0 UEFA Champions League Group E triumph.
Toure missed last weekend's 2-2 Premier League draw with Arsenal due to fatigue and question marks were raised as to whether he was ready to line up at the Allianz Arena.
But Cousillas said there was nothing wrong with the influential midfield lynchpin.
"On Saturday he didn’t play, but the reason was that he returned on Friday from the national team," he said.
"But he was absolutely fit (to face Bayern) and physically without problem."
City will be hoping Toure is firing on all cylinders when they host leaders Chelsea in the Premier League on Sunday.