I truly believe they respect each other on a high level.
Muller had a bad season in terms of scoring goals, but he still gave 100% when he played. Actually I thought he would explode under Carlo even more, because carlo is a pragmatic coach and Muller a pragmatic player like inzaghi back at AC Milan...
Also Carlo played him in the first period of the season in the 4-3-3 formation as right winger, which does not suit him, later Carlo changed it to 4-2-3-1 and gave Muller the chance to play as number 10 behind lewa, but that did'nt work aswell for him, later Carlo determined Thiago for his spot at Number 10, so there was no place anymore for Mulller.
Lewa
Ribery Thiago Robben
Vidal Alonso
Alaba Hummels Martinez Lahm
Neuer
Muller is not a winger or number 10, his best position is right behind the Striker, hanging striker so to say... thats the main reason for his average season