Frenkie de Jong’s red card saw the visitors play the last 25 minutes with 10 men, with Koeman dismissed in the dying seconds for dissent.
Barcelona now have just two wins from five La Liga matches as speculation mounts over Koeman’s future.
Memphis Depay went closest for Barca, miskicking from just yards out.
But it could have been worse for a visiting side lacking any creativity, as they needed goalkeeper Marc-Andre ter Stegen to pull off several impressive saves late on.
Koeman was left furious after two harsh yellow cards for De Jong in four minutes after the break led to Cadiz creating numerous late chances to win the game, having defended deep for the majority.
Alvaro Negredo, Salvi Sanchez and Anthony Lozano were all denied by Ter Stegen, while at the other end Depay was guilty of squandering several good opportunities for a Barcelona side lacking in quality but full of fight.
The frustration got the better of Koeman in injury time as he was sent from the sidelines for arguing against a late booking for Sergio Busquets.
One of the problems is in Spain they send you off for nothing,Koeman told La Liga TV. They don’t say why, they just say attitude. Everyone saw the moment there was a second ball on the pitch. Everyone has to see that.
I am strong of course. I can’t win the battle with the press. I will put my energy into the team and with the players. I still see a fantastic attitude of the players and for me that is most important. I can’t stop what the press are writing. We have to continue, that is my job.