The result extended Barcelona's winless streak to three matches and increased the pressure on Koeman. Koeman was sent off deep into stoppage time for complaints directed at the fourth official.
The Spanish football federation determined that this merited a tougher two-game suspension than the automatic one-game ban for a red card.
One of the reasons that upset the Dutch coach was the sending off of midfielder Frenkie de Jong after a second yellow card earlier in the match.
Barcelona argued that De Jong touched the ball before contacting his opponent and shouldn't have been booked.
Koeman said "in this country they send you off for nothing.''
Koeman has been publicly at odds with Barcelona president Joan Laporta, and on Thursday players showed that they are not on the same page as the coach either after he said Barcelona has no significant chance of winning titles this season.
Koeman made his comments by reading from a prepared statement in the pre-match news conference on Wednesday, something that caught the players and Laporta by surprise.
Sources have previously told ESPN that the club have explored options to replace Koeman, but the lack of available alternatives has prevented the club from acting hastily.
Koeman was hired by former president Josep Bartomeu shortly after the team's embarrassing 8-2 loss to Bayern Munich in the quarterfinals of the Champions League last year.
The Catalan club is playing without Lionel Messi for the first time in nearly two decades after he joined Paris Saint-Germain because of Barcelona's financial struggles. They also lost forward Antoine Griezmann to Atletico Madrid.
Barcelona are in seventh place in the league with nine points, seven behind leaders Real Madrid with a game in hand. They visit Benfica next Wednesday in the Champions League after opening their European campaign with a 3-0 home loss against Bayern Munich.
Information from The Associated Press was used in this report.