Kane scored from the spot to double Spurs lead in the 40th minute – following Christian Eriksens opener – before Alexandre Lacazette dragged the Gunners back into the game with a classy solo effort on half-time.
Arsenal found an equaliser as Pierre-Emerick Aubameyang prodded home Matteo Guendouzis pinpoint ball in the 71st minute, but their hard work looked to have been in vain as Sokratis Papastathopoulos appeared to shove Kane to the ground inside the box at the death.
However, Atkinson waved away the Tottenham captains calls for a spot-kick and the points were shared at the Emirates.
Asked about the penalty claim, ex-Chelsea and Manchester United manager Jose Mourinho told Sky Sports: Ive seen penalties for less but I dont think so.
Without the VAR i would say no for sure. With the VAR now, everybody is at risk.
In the other countries where the VAR has been in practice for a couple of years, like Portugal and Germany, Ive seen worse.
Former Arsenal and Spurs defender Sol Campbell added: I think, once you get in the box, obviously the forward is in control so you have got to be be careful.
He does come across to shield the ball but maybe a little too much and obvious but you do run the risk.