Lawrie Dudfield failed twice from the penalty spot, and scored once, as the Bees grabbed a point to deny Notts back to back home wins.
Dudfield's first opportunity came after sixteen minutes, but his effort was saved by Rob Burch, only for the referee to demand a re-take. Dudfield lashed that one in, and was given a chance of gifting Notts a two-goal advantage on the 35th minute, again he missed, hitting the bar.
Notts were left to rue the missed opportunity as Barnet's Captain Nicky Bailey tapped home from a corner to grab a point on the 74th minute.
Thompson kept faith with the 4-3-3 formation employed at Hereford, and in the previous home win with Torquay.
This was supposed to bring the best out of Notts' attacking play, but neither side started well. It was a scrappy affair, with referee Rob Lewis consistently pulling players up for fouls.
The stop-start nature of the game didn't help the tempo, and it wasn't until the sixteenth minute that the first opportunity was created, and that was just a half-chance. Good work on the left saw Dan Martin, McCann and Dudfield exchange passes and McCann cross to earn a corner.
Jay Smith chipped the flag kick in, and Burch failed to grasp under the pressure of Jason Lee. Notts' top scorer, who took over the Captains armband for the night, attempted to head a loose ball goalwards but Burch regained his footing to catch the ball.
Barnet's first real foray saw a long through ball test Pilkington's ball skills, as he was forced to race out of his area to stop former Mansfield man Adam Birchall racing through. Pilkington could only clear to Andy Hessenthaler who attempted to lob him. Fortunately for the Magpies, Mike Edwards managed to get back and head off the line.
Then came the first of three penalties. A rare good footballing move saw Martin release Andy Parkinson, whose pace and trickery took him away from Adam Gross, who could only trip him in the penalty area. The referee had no choice but to point to the spot, despite Gross' protests.
Notts' fans, in a dismal crowd of 3,010, were puzzled as to who would take it, with Notts' only previous penalty this season missed by Martin, ironically in the 3-2 win at Barnet. Dudfield, in fine recent form, stepped up, but his casual kick was easily saved.
Luckily, he got another chance, with Burch alleged to have stepped from his line. Despite Lee and McCann asking Dudfield for the responsibility, the front man showed nerves of steel to finish home and give Notts the lead. It was his first home goal for the Magpies.
Despite the best attempts of lively winger Barry Cogan, who was enjoying a good tussle with McCann, Barnet still couldn't muster a chance to warm their travelling support of just 143 on a chilly Meadow Lane night.
Notts began to show signs of upping the tempo, and Martin was again involved in a neat move. He found Lee, who laid it off to Smith. Smith managed to beat Hessenthaler to the ball and poke wide to Silk, who had advanced and found space. He whipped in a powerful ball, but the onrushing Notts attack failed to get a touch that could have posed problems.
A direct ball to Parkinson saw him release Lee, who lashed over the bar from twenty yards.
Cogan then released visiting forward Jason Puncheon down the line. Puncheon, wanted by a host of scouts, fizzed in a cross right across goal that evaded everybody. As with Silk's attempt, any touch would have been vital.
Notts were determined to avenge the miss, and Lee laid the ball off to Smith who advanced into a dangerous position, only to shoot without power into the arms of Burch.
Barnet's first corner of the game came in the final minute of stoppage time. Puncheon crossed and a scramble ensued, only for Joe Devera to shoot well over.
Notts were the first to attack in the second half, when a Dudfield and McCann one-two eventually won a free-kick near the left corner flag. Martin delivered well, and Lee, unmarked, volleyed at goal. Unfortunately he got too much lift, and should have at least hit the target.
Martin then won the ball well and found Parkinson, who, despite losing the ball, showed good determination to win it back and shoot early, though he failed to catch Burch off guard.
The two most experienced performers, Lee and Hessenthaler who is now 41, then tangled, with Lee earning a caution for persistent infringement.
Smith then seized on a loose ball to hit a swerving volley at goal that only just missed the target, so close that it hit the side netting.
This seemed to finally spark the visitors into life, and the industrious Hessenthaler began to break things up in midfield.
On the seventieth minute Bailey released Birchall into the clear, but he rushed his shot straight at Pilkington, despite being through.
A minute later Puncheon dribbled his way into the box and past a couple of defenders, only to see his shot lack power.
On 73, Bailey hit a free-kick against the wall, with the ball deflecting just wide of Pilkington's goal. From the resulting corner Bailey equalised. With Notts failing to properly mark, even with four men on the goal line, Bailey slotted in from three yards.
Bailey's evening got a little worse when he was rightly booked for a poor challenge on Martin, after some neat footwork from the Notts man.
With ten minutes left, Thompson replaced Martin with Junior Mendes, who remains far from 100% fit, whilst Barnet withdrew Puncheon for Oliver Allen.
Dudfield was cautioned for a harsh challenge on 83.
Silk steamed into the box on 85, and crossed to the back stick where Dudfield attempted an overhead kick that lacked power.
In the final moments Mendes surged down the right beating two players and crossing. His ball forced a corner, and Smith delivered well, only for both Parkinson and Mendes to fail to hit the target.
The draw meant it was now 26 points dropped at home for Notts, though they remain in eighth. It makes the derby with Lincoln on Saturday a must win, as Thompson acknowledged afterwards.