Inherited money from deceased father's qualified retirement plan and did a direct rollover (lump sum) to my employer's profit sharing plan 401(k). Do I pay taxes on it?

Can you clarify what type of qualified retirement plan you inherited?  The options for beneficiaries vary depending on the type.

You are not permitted to have rolled this distribution over to your own 401(k) account.  Doing so likely constitutes a failed rollover, a taxable distribution from your father's 401(k) and and an excess contribution to your own 401(k).  The only permissible rollover was a direct rollover to an inherited traditional or Roth IRA for your benefit, but that apparently is not what happened.