Yes, you can get a tax credit on your NJ resident return for paying local tax to a PA municipality. NJ doesn't have reciprocity with PA localities; it only has it with the state of PA. You just can't get a credit for paying Pennsylvania state income tax.
From NJ instructions, page 44:
http://www.nj.gov/treasury/taxation/pdf/current/1040i.pdf
Income From Philadelphia or other Pennsylvania Municipalities. The Reciprocal Agreement between Pennsylvania and New Jersey (see “Income From Pennsylvania” above) does not apply to the wage or income tax imposed and col lected by the City of Philadelphia or any other municipality in Pennsylvania. Therefore, income subject to both New Jersey income tax and any municipal wage or income tax may be included on Line 1, Schedule A.
The local tax credit is addressed in Turbo Tax in the Credit for Taxes Paid.
The example below uses Philadelphia, but the gist is the same if its not Philly.
https://ttlc.intuit.com/questions/3484428-philadelphia-wage-tax-is-a-credit-that-almost-covers-your-...
As far as not seeing a benefit on your return, its possible that you are entering it wrong. We can't see inside your return to see all the particulars of your income and how you addressed this, but you certainly are permitted this credit.
