The Spurs captain, who had already scored one spot-kick in the Premier League clash, went down under a challenge from Sokratis Papastathopoulos in injury time at the Emirates Stadium.
Referee Martin Atkinson gave nothing but Kane denied going to ground too easily.
The England striker told Sky Sports: “I think it was that stage of the game where he makes a tired tackle.
“I think if I am on the halfway line I get it, if I’m in the box it’s 50-50. The ref probably thinks I am looking for it but all I’m trying to do is shield the ball.
“But it is what it is. It’s one of them. It could be given in some games but it wasn’t today. You get on and move on.”
Spurs had led 2-0 after Kane added to an early Christian Eriksen strike but Arsenal hit back to claim a point through Alexandre Lacazette and Pierre-Emerick Aubameyang.