The Spanish midfielder entered the Wembley pitch in the 63rd minute of Manchester United's Community Shield clash with Leicester City on Sunday only to be replaced by Henrikh Mkhitaryan in the third minute of injury-time.
BBCMatch of the Day pundit and former Liverpool midfielder Murphy felt Mata was treated poorly by Mourinho and has implored the Red Devils boss to inform the 28-year-old if he has plans for him or not for the season ahead.
"My short version of it is him (Mourinho) letting the player know and letting everybody else know that he doesn't really have any plans for him any longer," Murphy said after United's 2-1 win.
"He's embarrassed the player in front of the fans, he's embarrassed him in front of his family and friends and I don't like that at all.
"I think Mata dealt with it really well, stayed on the pitch for the celebrations, did the right thing but I don't think he'll be in a Manchester United shirt come the end of August."