Do I need to enter a 1099-K from Eventbrite if I spent the full amount of the payout (revenue) on event expenses?

Yes, you'll report the amount of income that is on the 1099-K along with the event expenses on Schedule C of Form 1040.

I do not know what Turbo Tax version you are working with, so I can't tell you if you have to upgrade to Turbo Tax Self Employed or if you already have it. You will not be able to enter the income and expenses if you are using Turbo Tax Free Edition, Deluxe, or Premier. Once you either upgrade to the Self Employed version, or start working in your already purchased Self Employed version, follow these steps in Turbo Tax to enter your business income and expenses...

• Log into your tax return.
• Use the search box in the upper right hand corner. Type "schedule c" in the box and press enter.
• This will bring up the "Jump to schedule c" link...click that link.
• From here Turbo Tax will ask you some specific questions about your business. You'll be led through different screens asking you more questions regarding your business.
• Once you've answered these questions Turbo Tax will bring you to a screen to enter you income. This may be in the form of 1099s or no 1099s. 
• After you've added your income (or skipped that part) Turbo Tax will bring you to the screen for you to choose what expenses you would like to enter onto your tax return.