Can you deduct losses on your 401k on yearly tax return?

No these amounts are only paper losses and you never have reported the deferred compensation amounts on your 1040 Federal income tax return as taxable income and never paid any income taxes on the amount so you do not have any cost basis in the 401K plan YET and these transactions losses or gains are only taking place inside of the 401K plan each year.

This is the same thing that happens in the year that you have gains inside of your 401K plan you do NOT report the amount of gains as taxable income on your income tax return either because the transaction are taking place INSIDE of the 401K plan.