Enable "standby mode" for MacBook Pros
I don't think it's supported on your 13" MacBook Pro. From the KB article you linked (emphasis mine):


  Apple Portables that support standby mode are:
  
  
  MacBook Air (Mid 2010) and later
  MacBook Pro (Retina, Mid 2012)
  


I parse the text in italics to mean the Mid 2012 Retina MacBook Pro, not "Mid 2012 MBP and Retina MBP". This is further corroborated by the reference to the flash storage later on, which is only included by default on the MacBook Air and Retina MBP.