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But former United defender Higginbotham admits the scenario is different because Mourinho is criticising Shaw in public.
Luke Shaw has made just 18 Premier League appearances for Manchester United since Mourinho arrived at the club in 2016.
The England international has repeatedly been lambasted by his manager in press conferences and interviews.
The latest incident came at the weekend when Shaw was dragged off at half time of United’s 2-0 FA Cup quarter-final win over Brighton.
It is a football club that has constant pressure on the players and you have to deal with the criticism
Higginbotham came through the United academy so knows all about the pressure of playing for the club.
He says Shaw must deal with it but also believes Jose Mourinho has gone too far by making it public.
“I was fortunate enough to grow up at Manchester United and see the characters there and you have to deal with these things because the players have to be at their best all the time," Higginbotham told talkSPORT.
"It is a football club that has constant pressure on the players and you have to deal with the criticism.
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"The one thing we are not used to seeing is a manager being critical about a player in public and that probably makes it a little different.
"The fact he has got a year left on his contract after this season makes it more difficult for the club as well because his value is going to go down.
“It is not a good situation for the club or for Luke Shaw at the moment."