I was thinking more like depreciating the value of your car according to whatever depreciation schedule the IRS allows, prorated by the proportion of the miles you drive for Uber.
Something like - your car cost $30,000 and depreciates over 10 years, so $3,000 per year (just making up numbers, no idea if/how the IRS depreciates a car). So you'd have a $3,000 loss in the value of the car per year until it drops to 0. If the car was used 40% of the time for business (driving for Uber) you could claim 40% of the depreciation - $1200. I guess then you'd have to separately itemize all the gas, maintenance, etc.
But if you're actually losing money on the Uber-driving endeavor when that is factored in, whatever revenue you get should be tax-free. Of course, I suppose that only works if you're an independent contractor / business, and Uber drivers fought so hard to get treated as employees instead. Oh well. Employees get screwed when it comes to taxes.