According to Apple, you're using the right adapter (the MagSafe 2 connector). According to this page, the MBPs that you should use are:
85W MagSafe power adapter with MagSafe 2 style connector
- MacBook Pro (Retina, 15 inch, Mid 2015)
- MacBook Pro (Retina, 15-inch, Mid 2014)
- MacBook Pro (Retina, 15-inch, Late 2013)
- Macbook Pro (Retina, 15-inch, Early 2013)
- MacBook Pro (Retina, Mid 2012)
and
60W MagSafe power adapter with MagSafe 2 style connector
- MacBook Pro (Retina, 13-inch, Early 2015)
- MacBook Pro (Retina, 13-inch, Mid 2014)
- MacBook Pro (Retina, 13-inch, Late 2013)
- MacBook Pro (Retina, 13-inch, Early 2013)
- MacBook Pro (Retina, 13-inch, Late 2012)
If your MBP still isn't charging, try the SMC reset (as mentioned by @LangLangC) and/or bring it into an Apple store to confirm whether the problem is with your laptop. Another thing to try is finding a friend/co-worker that has a MagSafe 2 adapter to confirm whether your power charger is working.