Some players will rise to the critics and prove them wrong,  or try to improve themselves,  others will buckle under the pressure and hide away.   Which do you want?
If I underperformed at work I know I'd be told in no uncertain terms,  and if I didn't improve I'd be "managed" out of the business,  not paid till the end of my contract like a molycodled footballer.
Do you think it's a coincidence that the team has performed so much better under a manager who experienced life under Sir Alex Ferguson?
Success is available to those who fight for it,  anyone who buckles under a bit of harmless booing isn't worthy of it.
If your happy with second tier mediocrity then carry on,  but that's all you'll get.