Does a loss to a Roth 401k at the end of the year cause a reduction in taxes

No. Events within your retirement plan are not reflected on your tax return unless you have a withdrawal. 

No.  It is a tax deferred (and potentially non-taxable) account.  Gains are not taxable and losses are not deductible.  A loss in your account, whether realized or unrealized will have not impact on your tax return.    

There was a withdrawal

If you took a distribution from your Roth IRA and you are under age 59 1/2, or you haven't had a ROTH IRA for at least five years, then your distribution will be subject to an early withdrawal penalty.   Your withdrawal won't be subject to ordinary income tax unless your removed more than your cumulative contributions less previous withdrawals.  An early withdrawal with no hardship exception is subject to a 10% penalty on the amount of the withdrawal.