Worcester hit back after 19 minutes with a try from young back row Jake Abbott, which was converted by Loki Crichton.
Leeds scored again in the rearranged clash before the break through Andrew Boyde and Greendale slotted two more penalties.
Warriors staged a brave rally with tries from centres Greg King and fit again Dominic Feaunati, with Joe Carlisle adding a conversion, but narrowly lost out.
"We were frustrated because we started slowly and lost a bit of discipline and ended up with a few players in the sin bin," said Stan. "That left us 21-7 down after 20 minutes and we were always chasing the game then.
"Although we made a concerted effort in the second half we left too much to do to put pressure on them. But for a few lost possessions we might have done it and comeback.
"Now we look forward to the final game with Sale Sharks and a final flourish to the season for the team. Hopefully we will have a big crowd here at Sixways Stadium for the final game of the Guinness A League campaign and we can give them a really good send-off."