I typically ignore it. And the person.
totally ignore them
That's not your problem, it's theirs. Why are they resentful towards you?
Are you married to him? Have you tried marriage counseling? If something you did or said hurts him, and he wants to educate you to prevent further pain, I wouldn't characterize that as 'criticism'. Listen to him and stop hurting him in whatever way he tells you. Feelings are not right or wrong, they just are. If he feels hurt by something you said or did, that's enough. You should be free to tell him when he hurts you so this should be a two way street.
As with everything, it's always easier said than done. No one likes to be told what they've done wrong or that they were hurtful. Best wishes to you and your partner!
You have no control over what others think of you.