Taking the standard deduction vs. itemizing are merely two different methods to determine your tax liability.
But once you know the amount of your tax liability, you can apply tax credits as "credit" toward paying that liability.
Not owning enough to itemize doesn't mean you can't use the credit. It is not a tax deduction... deductions can only be applied if you itemize. Credits can be applied whether you itemize or not.
Note that if your tax liability is low enough that the credit is worth MORE than your liability, there is no cash-back nor can you carry the excess forward to be applied to next years taxes. It is a "use it or lose it" thing.
The IRS did apply an income cap. I think (so don't quote me) it's $150k for single filters, $300k for married (joint income), and head-of-household raises those limits a bit. If a person were single and making $149k they could claim the whole credit. If they make $151 ... they get nothing.
If you bought the car last year and didn't claim the credit this year (because you didn't think you could), consult a tax professional -- you may be able to file an amendment to your taxes.