Bartley scored two second-half headers to give the Blues their first win since October 1 and extend Huddersfield's run to one league victory in eight.
Booked for a challenge on striker Danny Ward, Bartley received a second yellow from referee Gavin Ward for taking a step over the advertising hoardings after putting Birmingham 3-1 up in the 81st minute.
The 22-year-old said: "It's a little bit bittersweet.
"I'm very happy to get the two goals and for the team to get the three points, but the red card means I'll miss the next game against Blackpool and that's massively disappointing to me.
"I've just got back into the swing of things and I won't be able to play another game for about a month now. I didn't touch my shirt and didn't go into the crowd but apparently I took one step beyond the hoarding.
"I knew he wasn't going to change his mind so I did the right thing and walked off the pitch.
"I'm devastated but if it's in the rule book, the referee has to do his job."
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