The Dutchman had already been under pressure following the return of president Joan Laporta with the pair not seeing eye to eye, but that relationship has deteriorated in recent times.
Barcelona finished the 2020-21 season in third in La Liga and were eliminated from the Champions League in the last 16. Koeman did lead them to lift the Copa del Rey.
Blaugrana are currently sixth in La Liga with 12 points from six games, although they have a game in hand on the sides above them, but their European struggles are concerning as they struggle forward without Lionel Messi.
“I’m not going to discuss the level of this team,” Koeman said post-game.
“Everyone knows what Barcelona’s problem is today. It’s not possible to comment on a team that’s not the one of past years. For me it’s clearer than water.”
The Dutchman would also not be drawn on his future amid the constant speculation which has engulfed in existence in recent weeks.
“I can only comment on my work with the team,” Koeman said. “I feel supported by my players and the attitude (theyve shown me).
“I dont know about the rest. I dont know about the club. I can’t say anything about my future because I dont know how the club thinks in that sense.
“I dont want to answer any more questions about this because it’s not in my hands. Well see.”