City were more than competitive in the first-half and created the better chances but their good work unravelled as the game approached half-time.
Emi Buendia was dismissed on 35 minutes for a coming together on Ashley Westwood and he was followed to the dressing room ten minutes later by Josip Drmic who was shown red for a late lunge on Erik Pieters.
Speaking post-match, Farke said: “We are sitting in position 20 in this league. We finished the last home game with eight outfield players. I'm far from accusing anyone else.
“In these moments, we have to look in the mirror and have to say these two red cards were naïve, inexperienced, unprofessional, stupid – to be honest, all the words fit. One thing is for sure, these two red cards are not acceptable at this level.
“To finish a game with just eight lads, you can have the best team in the world and it wouldn't be possible to win any points at this level."