On your end, "accepted" means your tax return was accepted for processing. It does not mean they accepted your payment or received your payment of tax due. How did you pay? If you expected to pay from a federal refund, that is impossible. Most states want you to pay with a check or money order, or by going on the state's own tax web site and paying with a credit/debit card. If you have no bank/credit card records showing that you paid, then you still need to pay your state tax.
Accepted means the electronically filed tax return was received by the state tax authority without errors that would have caused the return to be rejected. It does not mean that a payment was received by the state.
In the File section of the TurboTax program in Step 2 there were several options on how to pay the state taxes owed. How you chose to pay the taxes will be shown in the Filing Instructions page for the state tax return. Note that payment of taxes owed from a tax refund, Federal or State, is Never an option.
If you do not have a cancelled check, bank or credit card statement showing the taxes paid then no payment was processed by the state.
Review the State Filing Instructions page -
When you sign onto your online account and land on the Tax Home web page, scroll down and click on Add a state.
This will take you back to the 2018 online tax return.
Click on Tax Tools on the left side of the online program screen. Then click on Print Center. Then click on Print, save or preview this year's return.