Kane went down in the penalty box in injury time under a tackle from Sokratis Papastathopoulos, but his claims for a spot-kick were waved away by referee Martin Atkinson, a decision upheld by the subsequent VAR review.
Kane had scored Spurs’ second goal from 12 yards, putting them 2-0 up, after a rash challenge on Son Heung-min by Granit Xhaka. Christian Eriksen opened the scoring after a defensive calamity by the Gunners.
Alexander Lacazette pulled one back before half-time and Pierre-Emerick Aubameyang equalised in the second period for Arsenal.
Kane thought the foul by Sokratis may have been given in another part of the pitch, but didn’t say it was a clear-cut penalty.
"The defender made a tired tackle. On halfway I think I'd get that foul,” Kane told Sky Sports after the final whistle.
“Ref probably thinks I'm looking for it. It is 50-50, I could get it in some games."
Spurs now have two points from their last three Premier League games, with Sunday’s draw coming off the back of a shock loss to Newcastle last weekend. They had drawn 2-2 with Manchester City before the game with the Magpies.
The England captain said he was disappointed to leave the Emirates Stadium with only one point, but blamed his team’s lack of a killer instinct for the setback.
"I'm a little disappointed," he went on.
"When you go 2-0 up you expect to win whoever you are playing. The goal before half-time changed the momentum.
"Second half it was two teams going for the win. They were on top at times but we still had chances. All in all it is a point and we need to accept it.
"If a few final balls would have been better, we would have created more. It is a shame we couldn't kill it off. But it is the Premier League and if you don't kill teams off they come back at you."