Memphis Depay scored Barcelona s opening goal against Alaves on Saturday (AFP)
Xavi Hernandez is expected to be appointed Koeman's successor this week but with the details of his move still to be agreed with Qatari side Al Sadd, Barca B coach Sergi Barjuan has been put in temporary charge.
Yet the removal of Koeman, and even the prospect of Xavi, produced no obvious uplift as a superb second-half strike from Memphis Depay was quickly cancelled out by an equally impressive run and finish from Alaves' Luis Rioja.
After three league games without a win, Barcelona are eight points adrift of leaders Real Madrid, who earlier defeated Elche 2-1 thanks to two goals from Vinicius Junior and aided by a red card for Elche's Raul Guti.
Even more worrying for Barca will be the gap behind the top four is five points while attendances suggest the team's form is creating a sense of apathy amongst supporters, with only 37,238 inside the 99,000 Camp Nou.
There were also injury concerns ahead of Tuesday's visit to Dynamo Kiev in the Champions League, which could prove pivotal to Barcelona's hopes of reaching the knock-out stage.
Gerard Pique had to go off in the last 20 minutes while Sergio Aguero departed in the first half after the striker appeared to suffer from breathing problems.
Whether Barjuan is still in charge for the trip to Kiev remains to be seen but club president Joan Laporta suggested that is the current plan, with Xavi, or the next coach, perhaps taking over for next weekend's game against Celta Vigo or during the international break.
Barjuan admitted on Friday that it is "difficult to change things in a short time" but also said the team's style, a key factor in Koeman's dismissal, is "non-negotiable".
But while the first half an hour was perhaps slightly more purposeful, Barcelona still struggled for chances and their defence was beaten too easily for Rioja's equaliser.
For all the talk about style and possession, Depay's opener was a thunderbolt out of the blue. Jordi Alba played inside and Depay opened up his body before curling the ball into the top right-hand corner.
But Barca's lead lasted less than three minutes as Alaves equalised with another superb goal, Rioja dancing past three Barca defenders, latching onto a sublime flick from Joselu, before rounding Marc-Andre ter Stegen and finishing.
Depay was slipped through by Gavi and Nico Gonzalez but hit the post and then Antonio Sivera as Alaves held on for a hard-fought point.