Again, this is all part of the grieving process - wondering if the situation was your fault, and if it will happen over again.
I personally steer clear of concepts like 'fault' in relationships - it is a complex set of circumstances, and not easily reduced to a notion of someone's 'fault' as the reason for its end.
Similarly, your new relationship is a complex set of circumstances, but based on your experiences, you will be well placed to avoid the pitfalls of the last one, and should preoceed with cautious optimism.