As quoted by the official Bayern Munich Twitter page Kovač said: "We started well in the first ten minutes and then made too many individual mistakes. And then we concede goals like that. Three shots, three goals."
Alassane Pléa combined well by Jonas Hofmann to curl home the opener for the away side in the ninth minute, before Lars Stindl found the bottom-corner after Hofmann dispossessed Thiago. Substitute Patrick Herrmann added a third in the latter stages of the match, but Kovač insisted that the damage was already done in the first-half.
He added: "Congratulations to Borussia Mönchengladbach. The goals in the first half unsettled us. We have to live with the defeat."
Another blow for the Bundesliga holders was the departure of David Alaba through injury. The Austrian limped-off and was replaced by Renato Sanches nine minutes into the second-half.
He added: "I spoke to David briefly. I think it could be a strained muscle, but we need to see what the tests say."
Following the international break, Bayern travel to eighth-placed Wolfsburg. However, with increasing criticism, the Croat may be fortunate to still be in charge by then.