The scoreline was 2-2 in Turin before Bonera's shocking leg-breaker challenge earned him a straight red card on 66 minutes and Juventus went on to win 3-2.
"I went by the locker room earlier to apologise to Sissoko, because I realised I had made an awful tackle," confessed the defender.
"I wanted to get the ball and was already powering in. I should have stopped, but I was going at some speed and looking back at the footage it was a horrible challenge."
Bonera is well aware his dismissal also proved disastrous for Milan, whose 3-2 defeat puts a huge dent in their Champions League chances.
"I apologised to my teammates too, but we should not have conceded on a set piece. We only suffered under a little bit of pressure after going down to 10 men.
"Clearly now we are forced to chase fourth place and hope other results go our way. We have to believe right up until the end, but time is running out."