Early 2011 MacBook Pro does not standby correctly
This Support Page at Apple does not specify your MBP as fulfilling the hardware requirements for using Standby mode:

•   MacBook (2015 and later)
•   MacBook Pro (2012 and later)
•   MacBook Air (2010 and later)
•   SSD and Fusion drive versions of Mac mini (2012 and later)
•   SSD and Fusion drive versions of iMac (2012 and later)
•   Mac Pro (Late 2013)