Mourinho criticised his fitness, focus, commitment and ambition at the weekend and then heaped further embarrassment on the England defender by claiming he had been his “brain” after bringing him on as a substitute in the draw with Everton.
But Shaw refuse to be bowed, saying: “Sometimes I tend to keep it low profile but obviously with the stuff that has been going on it is hard to take because deep down that is not me as a person.
“Like Jose said, he wants to see me fighting, and I will fight to the last second because I want to be here for the club.
Luke Shaw insists he will fight for his place
Mourinho has not held back in criticising Shaw publicly this week
“I am working really hard at the moment, now more than ever. I am going through a phase where everything is going against me, but I want this so badly, I want to prove everyone wrong.
“I want to play for the manager and I want to help this team get back to the top. I am keeping my head up and I am going to fight to the last. I am not going to give up.”
Shaw, who has started only two games since the end of November, says he has been encouraged by messages of support from United supporters.
He added: “It is easy for them to see those comments and turn on me. But they have been so good to me, especially over the last couple of days. It is something I won’t forget for a long time because it means a lot to me.
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“I don’t want to let them down and I’ll fight for each and every one of them.”
Shaw made an impact when he came on against Everton and it was his goal-bound shot that was handled by Ashley Williams to give Zlatan Ibrahimovic the chance to score the equaliser from the penalty spot in added time.
Williams’ action denied the former Southampton player his first senior goal but Shaw was just relieved United salvaged a point to stretch their unbeaten Premier League run to 20 games – although 10 of them have been draws.
And while Shaw will not give up his battle to convince Mourinho, he says United will not concede their top four hopes are over after their ninth home draw of the season.
Shaw played just his second Premier League game of 2017 on Tuesday
“We were unlucky,” he said. “Sometimes the luck is not in our favour. We’re all disappointed in the changing room, but we’re not going to give up, we’re a team of fighters and experienced players.
“There is still a very good chance of reaching the top four and that is our aim right now.
“Obviously we’re still in the Europa League, that is another positive. If you look at the teams in it, we can be one of the favourites. We know we have got the quality and determination to win it.”