Defeat for the Hoops, just their fourth ever at home in the group stage of the competition, leaves them bottom of Group C and with little hope of reaching the last 16.
Toure failed to usher the ball out for Gladbach's deserved opening goal, which Lars Stindl in turn blasted home, while also being caught out for the second as Andre Hahn was played in to seal the victory for his side in Glasgow.
"I have to blame myself," he told BT Sport. "It was a simple action to put the ball to the side [for the first goal], but I like to keep the ball in play.
"Over-confident? For the second goal it was the same thing. I don't like to make mistakes but mistakes happen. I'm 35 and making a mistake like a 16-year-old."
Celtic face Gladbach again in Germany on November 1, with their aspirations now resting on finishing third and qualifying for the Europa League.