There's no way to claim the expenses without reporting the income, which you're required to do.
However, you'll only pay self employment tax on the "net" income, meaning the amount left after deducting your expenses. So if you had a net loss, you will not owe SE tax.
Assuming your business is a sole proprietorship, you'll need to use TurboTax Self Employed online to report your income & expenses. TurboTax will prepare a Schedule C form (Profit or Loss From Business) and include it as part of your individual tax return.