This is definitely possible, but surely is not always the case. Sometimes, as we know, people are unjust to us and our disappointment within ourselves is not the cause of our anger toward these people .Yet, if you sense that Person A, someone you wish to help, is continually finding fault with many people and your sincere judgement is that these others are not behaving nearly as badly as Person A is saying, then yes, your plan of action seems reasonable. Gently ask Person A if she is dissatisfied with herself, perhaps she has broken her own standard. Self-forgiveness then may be the best place to start.
Learn more at Self-Forgiveness.