I'd argue you still have responsibility for your government's actions, regardless if you voted for them. Your responsibility as a citizen is to hold your government accountable, whether that's by voting, writing letters, talking, protesting, or (in the extreme case) civil disobedience or rebellion.

Unfortunately, the more important it is to hold your government to account, the harder it is. I, personally, don't have the strength to do that, for all I talk of it.