Substitute striker Michael Symes had volleyed home his eighth goal of the season six minutes from time for what Peters thought was a much needed three points.
But Stanley's Robbie Williams scored a late goal to salvage a point for the Reds and halt their run of five successive league defeats.
It was an entertaining game from the off with Town awarded a penalty on three minutes when nippy striker Derek Asamoah was pushed by Leam Richardson in the area and Asamoah sent keeper Ian Dunbavin the wrong way for a dream start.
The Reds felt they should have had a penalty of their own when Andy Proctor was fouled a few minutes later, but it was waved away by referee Eddie Ilderton.
However, the official did point to the spot on 18 minutes when Paul Mullin was caught by Shrews midfielder Stewart Drummond in the area.
Winger Andy Todd sent the penalty straight down the middle for his fifth goal of the season.
Defences were on top after that with neither keeper seriously troubled until the 40th minute.
Then Dunbavin made his own problems by kicking the ball straight to Shrewsbury's much-travelled striker Leo Fortune-West. The hitman dribbled past the keeper and, despite a last-ditch tackle by Phil Edwards, the ball rolled into the net.
Stanley went straight up the other end and Mullin forced a save out of Scott Shearer, but boss John Coleman must have given his side a firm team talk at half-time as they came out battling.
Cardiff loan player Joe Jacobson had two early chances, one tipped over acrobatically by Shearer and a 30-yard effort which was deflected.
But he then played his part in the second equaliser on 54 minutes when his free-kick was headed home by Edwards for his first Stanley goal in a well worked routine.
Shrewsbury then put on top scorer Symes on 66 minutes as they looked to boost their attack and he was in the action immediately.
He drove in a fierce strike which Dunbavin did well to save and the follow-up by Dave Edwards was also kept out by the Stanley keeper.
Stanley threw on a striker of their own in substitute Leighton McGivern and he looked like he could be the Stanley hero after some tricky work on the edge of the area resulted in a goalbound shot, which Shearer did well to save.
But the visitors went straight down the other end with Asamoah racing past Danny Ventre and setting up Symes, who volleyed home from the edge of the area.
However, there was one last twist, when a long ball forward seemed harmless, but Williams was there on the edge of the area to neatly chip the ball over Shearer and rescue a much-needed point for Accy.