The Standard Deduction has nothing to do with your self employment expenses. The SE expenses reduced your Net Profit on Schedule C so you paid less SE tax on it. The Standard Deduction is subtracted from your total income so you have less income to pay regular income tax on. You are paying both regular income tax and self employment tax. You get to take both the Standard Deduction and your self employment expenses.
Business expenses are not reported on Schedule A as an itemized deduction.
They are entered on Schedule C. Business expenses reduce the amount of business income that is reported on your tax return Form 1040 as a net profit. Thereby lowering your taxable income and your tax liability plus reducing the amount of Self-Employment taxes you have to pay on the net profit.