Gomez complained last week that he was being substituted too often - and was promptly left out of the starting line-up altogether for Saturday's match with Bundesliga leaders Hamburg SV.
"I spoke with his agent a few days ago and told him that I advise Mario urgently to stop complaining," Bayern's general director Karl-Heinz Rummenigge told the Welt am Sonntag newspaper.
"When you play for Bayern Munich, you must work hard and give everything."
But their domestic form has been indifferent and Saturday's 1-0 loss at Hamburg SV left them a modest seventh in the Bundesliga with 11 points from seven games.
Juventus, who drew 1-1 at home to Girondins Bordeaux in their Champions League opener, again lacked a killer instinct in Sunday's 1-1 Serie A draw with Bologna where the visitors equalised in stoppage time.
With centre back Fabio Cannavaro injured, the defence has looked shaky and Gianluigi Buffon has often had to show why he is regarded as one the world's best goalkeepers.
Despite the few difficulties, Ciro Ferrara's side are the only undefeated team in Serie A.
In-form Italy striker Vincenzo Iaquinta was rested for Sunday's match but looks certain to return against Bayern with Amauri poised to partner him upfront despite failing to shine so far this term.
"I am convinced that this team, my team, can do better and will try to do better immediately against Bayern Munich," Brazilian midfielder Felipe Melo told the club's website.
