A stunning overhead kick from substitute Sam Hollis with 14 minutes remaining looked to have been enough to secure victory for Stamford against a visiting side who were reduced to 10 men following Richard Adams' 68th minute dismissal.
However, following what Drury described as a 'comedy of errors,' Sheffield snatched a 92nd minute equaliser when goalkeeper Dan Haystead saw his attempted clearance richochet off James Gregory and loop into the home net.
And Drury pulled no punches in a post-match assessment of the draw which saw Stamford slip down to 12th place in the EvoStik Division One South standings.
He said: "I am absolutely seething. Our man-management of the game has cost us.
"We were not at the races in the first 15 minutes or the last 15 minutes and that has cost us two points.
"We can forget about being in contention for the title and the play-offs if we perform like that.
"Sam Hollis has scored a great goal which should have won us the game, but a comedy of errors has let them back in.
"Mistakes happen at any level of football, but we should have managed it better and should have been good enough to have kept the ball against 10 men rather than going backwards.
"We started in first gear and, when that happens, you struggle to ever find fifth gear in a game.
"There was too much back-biting between the players and they will be getting a big shock at training on Tuesday because we have thrown two points away.
"There was no positives for me even though we've maintained our unbeaten home record because it's points that get you into good positions in the league table."
Stamford made just one change to their starting line-up following their FA Trophy victory the previous weekend with Joe Burgess replacing the unavailable Mike Armstrong.
However, a sluggish start saw Sheffield take the lead after just nine minutes when Tyler Williams cut into the penalty area from the right before rifling in a shot that took a deflection and looped over Haystead.
Stamford responded with Pearson Mwanyongo firing a long distance shot just wide while the lively Bradley Fortnum-Tomlinson saw an audacious first-time effort from Haystead's clearance land just over the bar.
Gregory, an early replacement for Alex Brown, then broke free in the box for the visitors but dragged his shot wide when well placed.
Haystead showed good handling to gather a shot from Ricardo German before Stamford got back on level terms six minutes before the break.
A long clearance released Fortnam-Tomlinson who left the Sheffield defence trailing in his wake before slotting home past the advancing Ben Ledger.
Sheffield almost regained the lead immediately though as Haystead made a cracking fingertip save to keep out a German header but, with the goal at his mercy, Ben Turner fired the rebound into the side-netting from a tight angle.
Eliot Putman then went close with a shot from a flowing Stamford move as the hosts finished the half in the ascendency.
Jake Duffy cracked an early second half effort narrowly wide while Jordan Smith had an effort blocked after Hollis - who had replaced Mwanyongo - had his timed his run to perfection to beat the offside trap.
Stamford upped the pressure as Rob Morgan saw his magnificent mazy run into the box create an opening only for his goalbound shot to be deflected over by a terrific last-gasp block.
The match looked to be swinging in Stamford's favour when Sheffield skipper Adams, as the last man, brought Fortnum-Tomlinson's burst clear to an abrupt halt and was red-carded.
The Daniels then took the lead eight minutes later when Fortnum-Tomlinson's cross picked out Hollis whose sublime overhead kick looked to have secured the points for the hosts. It was a goal worthy of winning any game, but unfortunately for Stamford they let the victory slip from their grasp in the second minute of injury-time.
The ball was needlessly played back to Haystead when Stamford were in possession and the home goalkeeper allowed Gregory to get too close before clearing and the ball rebounded off the Sheffield player and looped into the home net.
Stamford forced a couple of late corners in a bid to salvage the three points, but Sheffield held firm to pocket a priceless point in their battle against relegation while denting the Daniels' promotion aspirations.
# | Team | Pl | Pts |
1. | Basford United | 42 | 100 |
2. | Alvechurch | 42 | 85 |
3. | Frickley Athletic | 42 | 82 |
4. | Bedworth United | 42 | 74 |
5. | Chasetown | 42 | 73 |
6. | Stamford | 42 | 71 |
7. | Leek Town | 42 | 68 |