The Clarets recorded their first-ever win at the Emirates Stadium to compound the Gunners to a record fourth-straight defeat at home.
They picked up a point against Southampton on Wednesday - despite centre-back Gabriel's second half red card - but remain precariously in 15th position in the Premier League.
The defeat to Burnley was indisputably Arsenal's worst showing of the season and according to The Athletic, Arteta was so frustrated he decided to skip the post-match team talk and wait until the following day to launch an inquest into what went wrong for his side.
The report adds that some Arsenal players are growing disgruntled with Arteta for his preferential treatment of certain members of his squad.
Some are said to be frustrated that Willian kept his place in the XI for the visit of Leeds after the Brazilian broke the government's coronavirus guidelines by visiting Dubai during the international break.
Nevertheless, technical director Edu said Arteta maintained the full backing of the board earlier this week, insisted the Gunners' current slump in form does not coincide with the work that is being put in on the training ground.
Asked if Arsenal supporters needed to relax and not to worry, Edu - speaking in an interview before the Burnley loss - said: "Relaxing is too much.
"Just believe. Internally here, listen, we are doing well.
"My main message is that we are not talking about only one person, it is unfair to talk about Mikel, or Aubameyang because he is not scoring goals, or (goalkeeper, Bernd) Leno because he has to stop the goals.
"It is unfair to talk about one person, we are a football team, we have to talk about ourselves, talk about "we" and not "him" so that for me is the main message."
Arsenal boss Mikel Arteta was left so angry by his side's defeat to Burnley last weekend he did not speak to the players after the game, reports claim.