Those parameters are not taken into consideration if you are a resident of Massachusetts.
I am unaware of any state having an equivalent to the Foreign Earned Income Exclusion, or allowing a credit for taxes paid to a foreign state/ locality. In general, to minimize/ avoid state tax, you would have to no longer be a resident of Massachusetts. The federal government considers citizens and long term resident taxpayers for their whole lives (expatriation aside), but you are not tied to your "home state" forever. The link below remains on the MA tax site as a source for determining residency.
Since you were abroad all year, it will likely come down to whether or not you have a permanent home in the State of Massachusetts. Most states have a similar basis for residency rules.
Here's what Massachusetts considers a resident- apply this to your situation to determine if you have to file an MA return for the portion of the year that you were abroad:
If you have to file a Massachusetts return, the credit for taxes paid cannot be taken.
"The credit is not allowed for: taxes paid to the U.S. government or a foreign country other than Canada; city or local tax; and interest and penalty paid to another jurisdiction."