The Royals took the lead against the run of play through Jobi McAnuff's composed 39th-minute strike and though Birmingham levelled four minutes later through Paul Caddis' penalty, McAnuff popped up at the far post with an 82nd-minute winner.
Birmingham have now gone 14 games without a league win at home and are just five points above the relegation zone.
Clark said: "I feel really disappointed for the players because the one result that shouldn't have happened was a defeat for us.
"The minimum we should have got was a point. We played good stuff, we competed with a really good team and it's tough for the players to take. The slightest error seems to be getting punished at the moment.
"We have to regroup. There were a lot of positives to take from this but the lads are hurting and it's a quiet dressing room."
- Sports & Recreation
- Jobi McAnuff
- Paul Caddis