Non-deduction of TDS by the tenant does not shift the statutory liability onto you. Under Section 194-I of the Income-tax Act, 1961, the obligation to deduct TDS on rent (generally @10% for land/building, subject to threshold) rests solely with the payer (tenant). Failure to obtain a TAN or to deduct/deposit TDS attracts consequences for the tenant under Sections 201(1) and 201(1A) (being treated as assessee-in-default and liable for interest). You, as landlord, are not required to deposit TDS on their behalf, nor can you do so using their TAN. However, as per Section 191, your obligation is to correctly report the rental income and discharge tax thereon; if full tax is paid by you, the tenant may avoid being treated as assessee-in-default (though interest may still apply).
For return filing, rental income from commercial property is taxable under the head "Income from House Property" (Section 22), provided you are the owner. You should report the gross rent received/receivable, claim the standard deduction @30% under Section 24(a), and also claim interest on borrowed capital, if any, under Section 24(b). TDS credit is not relevant here since none has been deducted. The fact that rent is below Rs. 20 lakh and outside GST has no bearing on income-taxability.
In summary, there is no adverse consequence on you for non-deduction of TDS by the tenant if you have correctly offered the income to tax; the compliance default lies with the tenant.