The 58-year-old was left incensed in the dying seconds of the match after arguing with the referee and match officials.
Earlier in the game, Koeman was furious when midfielder Frenkie de Jong was shown a red card and tempers continued to flair until he was dismissed in the final stages.
It comes amid criticism of Barça’s form this season, with Koeman’s young side failing to gel after the departure of Lionel Messi.
The Catalan giants have won just twice in their first five league games, sit seventh in La Liga and were thrashed 3-0 by Bayern Munich in the Champions League.
Questions have subsequently been raised over Koeman’s future at the club and his relationship with club president Joan Laporta has reportedly become strained in recent weeks.
“It’s not always down to a result. We have to analyze what the team did, the attitude of the team, the commitment of the team and I can’t complain about any of that from this game,” Koeman told reporters after the match.
“I’m not happy, of course, because we had four or five clear chances and we didn’t score any goals.
“What I take away is the attitude, not my own personal situation. Because if we win, it looks like we carry on, and if not, we look for another coach – and that’s a question for you.”
Barcelona is already seven points behind rival Real Madrid in the league and looks a shadow of the side that dominated European football for years.
But the club’s financial situation has forced them to offload some of its biggest stars, most notably Messi who moved to Paris Saint-Germain when Barcelona was unable to afford his wages.
Attention has since been switched to bringing young talent into the first-team but such inexperience on the pitch has become a problem in recent weeks.
Koeman also lamented his side’s injury problems which prevented a number of senior players from playing against lowly Cádiz.
“You have to be realistic, look at the squad we have and the players missing,” he said. “We’ve got seven starters out.”