I withdrew my 401 K when I quit my previous job. Does that me I qualify to not pay the additional taxes?

[MaryK4]

No, unfortunately, leaving your job does not qualify as an exception to the penalty.  See An Early Withdrawal From Your 401(k) - TurboTax - Intuit.

[Opus 17]

If you are age 55 or older in the year you leave the employer, you are exempt from the penalty.  Less than that age, you are not exempt from the penalty.

You had the option of rolling over the money into another workplace plan or an IRA within 60 days.   The rollover would have been non-taxable and the money would have grown until retirement.  But since you took the cash, it is taxable plus a penalty.