Were you aware that blaming others is a form of emotional abuse? It hurts being on the receiving end of blame, and it causes a lot of stress in your relationships in general. Sometimes, it’s easier to blame another than take a step back and see your part in it. Sometimes, you err and don’t want to take responsibility for confusion caused by miscommunication, personal stress, or old patterns of victimization. It seems easier to blame someone else and feel justified in doing so, but freedom and growth come when you take responsibility for your actions and your mistakes. 
Forgiving yourself for being imperfect (we all are!) and others (for their imperfections, too) opens your heart and grows accountability in relationships. Forgiveness breaks down resentment and stops the “blame game”. Be honest with yourself, even when it bruises your tender ego, and admit your part in whatever causes the wobble within yourself or in relationship to others. It is important to note that what you think is happening “out there”, caused by another, is merely some area of hurt/unconscious reaction/pain happening inside that keeps showing up in one form or another. It will keep showing up, until it is healed. In your life, you are indeed the common denominator in all your experiences. Now is the time for reflection and to forgive. Gather all the broken, fractured pieces of yourself and forgive yourself. Forgiveness is the glue that helps you heal from the inside out. It’s time for healing and letting go of outworn modes of behavior and to move forward.
In truth, blame is a reaction of deflection that takes you out of present time, throws you back into childlike behaviors that does you no good, and reduces intimacy in your life. Obviously, it is difficult to feel close to anyone when they are blaming you, but instead of blaming others for blaming you, when you go within, you can observe the cascade of emotions and feelings running through your system. In times like these, we need all our wits about us. Observe, Breathe, Forgive and Ask for Forgiveness. Being human is not always easy. The cycle of blaming yourself, others and being blamed is never-ending unless you step outside the fray and let it go. What is most important is to save your mind. For those relationships that have value to you, take some time to step back from highly charged situations until you are able to express your feelings with less emotion. This way, there is an opportunity to deepen your connection and find solutions which are mutually beneficial when you do come together and talk. 
Here’s a great prayer I learned from my spiritual teacher. When you feel blamed, wanting to blame or blame yourself, say this prayer until the feelings subside:

I love you and I forgive you.

I love you, please forgive me.