The visitors found themselves 2-nil up following goals from Christian Eriksen and Harry Kane, but Alexandre Lacazette halved the deficit just before half-time.
Pierre-Emerick Aubameyang completed the comeback for Arsenal in the 71st minute, and the match looked bound to produce a winner.
Sokratis thought he had won the derby for the hosts only for his goal to be rightly chalked off for offside.
The Greek almost gave Tottenham their second penalty of the day after appearing to have tripped Harry Kane in the closing stages of the game.
However, referee Martin Atkinson waved play on, and VAR agreed with his decision.
“Martin Atkinson controlled a thrilling north London derby with great experience and it was an excellent decision not to award Spurs a penalty when Harry Kane went down late on,” Clattenburg told Sportsmail.
“Kane used his body and leg to initiate the contact with Arsenal defender Sokratis Papastathopoulos and it was not a penalty. VAR would have checked the incident but Atkinson’s on-field decision was correct.
“Should Kane be booked for simulation? I would say not as there is contact. I also didn’t think there was anything in the Dani Ceballos-Dele Alli clash. And again no need for VAR to get involved.”
Spurs can have no complains after replay showed there wasn’t a foul involved during the tangle between both players, but they will be disappointed to have seen a two-goal lead slip through their fingers.
It’s been a shaky start for Mauricio Pochettino’s men in the opening stages of 2019-20, with just a victory in four games.
Tottenham have lost one and drawn two others, and the international break has come at the right time for the squad.
Pochettino will look to press the reset button and hope his players can hit the ground running after the break when Crystal Palace come visiting.