Yes, you would need to itemize to claim your car donation.
TurboTax automatically selects the best deduction for you that will earn you the most money back. So, if the program is prompting you to take the standard deduction, most likely your car donation didn't outweigh that option.
For tax purposes, because a donation is a deduction from your income, the tax benefit relates to your tax bracket. It's not a dollar-for-dollar item.
For more information, please see the following TurboTax FAQ:
https://ttlc.intuit.com/replies/4201669