No, you can't deduct it. Under the new tax law, employee business expenses are not deductible for 2018 through 2025.
If the reimbursements were paid under an "accountable plan" they should not have been included in your W-2. An accountable plan has to meet a number of requirements. The most obvious aspect of an accountable plan from the employee's point of view is that you have to submit expense reports.
If your employer does not have an accountable plan, then the reimbursements are taxable income to you, and including them in your W-2 is correct.
But your description of what your employer did is a little vague. You said that the reimbursements were included in your paychecks, and that tax was withheld on them. But are you sure that the reimbursements were actually included in box 1 of your W-2? That's the real key. If they are not included in box 1, then you are not paying tax on them, even if tax was withheld on them.
As Critter suggested, if your employer does not have an accountable plan you should talk to them about the fact that employee business expenses are no longer deductible. A non-accountable plan worked okay prior to 2018 because you could deduct the expenses on your tax return, but that's no longer true.
