Josh Simpson gave the hosts the perfect start in the first minute, but goals from skipper Matt Richards and John Taylor put Shrewsbury in charge.
They looked to be heading for their first away win since Good Friday until Simpson rifled home from 15 yards to secure a 2-2 draw.
But Turner's men wasted a glorious opportunity to win in stoppage time when substitute Tom Bradshaw missed from four yards following a cross by Paul parry.
Turner rapped: "He gets no sympathy from me. He is paid to put them in.
"Sitting in the dressing room 30 minutes after the game the players would have felt heartened by the result.
"But realistically it's more of a feeling of devastation as a late goal that had been conceded and then a great chance to win the match had been wasted. It was a game we should have won."
He added: "Conceding early goals is happening too often. Players have got to acquire a winning mentality away from home.
"We allowed Crawley to dictate too much when we were 2-1 ahead. We invited pressure at times but at other times we passed it around well. We also should not be giving away silly free-kicks in our own half.
"But we have to take the positives from the game. We would probably have taken the point going into this match."