Though my company reimbursed some moving expenses which can be claimed as moving expense deductions, the amount reimbursed was not put on to my W2 form in Box 12... under P—Excludable moving expense reimbursements paid directly to employee (not included in boxes 1, 3, or 5)

Should I just mention the reimbursed amount by my company in my return or ask my company for a corrected W2

Please advise.

If your employer has reimbursed you the moving expenses, you can not claim them. You can only claim the difference if the actual expenses are more than the reimbursed expenses. Your U.S. Tax Return: Moving Expenses

Yes, you should talk to your employer.