Shaw was speaking about United's failure to position themselves higher in the Premier League this season.
United are ninth in the table, while Arsenal are one place back in tenth.
But he believes being a United player makes him more of a target.
"I've had to have a thick skin. Sometimes it's easy for people to forget what I've actually been through," he told The Mirror.
"You need to have a thick skin to play football anywhere, but especially at the biggest club in the world here at United. Everyone's watching and wants to have a go whenever you lose.
"They're just waiting to criticise the moment anything goes wrong but that's part and parcel of playing for United.
"No disrespect to Arsenal who are a fantastic club, but they're not exactly having the greatest of seasons and it's hardly mentioned.
"I find it quite funny that if it's United, everyone criticises, but Arsenal don't get a mention.
"Look, we know when we haven't been good enough and at times we haven't been. We all know why we're here.
"We're here to take this club back to where it belongs – winning trophies and challenging for titles. And I honestly believe we're on the way towards doing so.
"We know when we're not at our best and we know when we play well what we can achieve – but we have to sustain it that's why I believe there are a lot of good days to come."