Tony Mowbray’s side were fortunate to still be level at half-time after Anthony Patterson saved Joe Ralls’ penalty.
Cardiff took the lead four minutes after the restart, though, as Mark Harris converted Mahlon Romeo’s low cross.
The hosts did apply some late pressure but couldn’t force an equaliser.
1. Anthony Patterson - 7
Did his best to keep his side in the game with a brilliant penalty save and there was nothing he could do about Harris’ second-half goal. 7 Photo: Martin Swinney
2. Luke O’Nien - 5
Got into some good areas at the end but his crosses were never likely to yield a result once Simms was off the pitch. Defensively struggled to contain some lively Cardiff forwards. 5 Photo: Frank Reid
3. Bailey Wright - 5
Struggled on the ball and that led to the penalty. Made a number of errors in possession, perhaps three games in a week on his recall to the side catching up with him. 5 Photo: Frank Reid
4. Danny Batth - 5
Had little choice but to give the penalty away in the opening moments and wasn’t quite as composed as we have seen from him so far this season. 5 Photo: Frank Reid