Wouldn't taking the standard deduction of $12,000 have been better than itemizing which was $11,625. It was close but wouldn't I have gotten $375 more money back?

No, you don't get back the exact amount of a deduction, you owe less tax based on how much tax you would have paid on that amount of income.  For a deduction of $375, at a 10% tax rate, you might have gotten back $37.50 more or owed that much less.  I am sure, though, that your standard deduction was HIGHER than your itemized.  Itemized deductions can be subject to a subtraction of a certain percentage of your AGI.  Your standard deduction may also have increased due to your age.

Sounds like they got the itemized deductions instead of the higher Standard Deduction.  Did you pick to use Itemized Deductions?  Are you a dependent?  Or Married filing separately?  Turbo Tax normally gives you the higher amount.