The youngster went down inside the West Ham penalty box under a challenge from Barcelona-owned former Arsenal midfielder Alex Song.
Kane picked himself up and tucked in the rebound after West Ham goalkeeper Adrian had managed to save his initial spot kick.
The penalty decision was controversial and one which Allardyce did not agree with, taking a dig at Kane for going down easily.
"You can argue whether Alex Song has made enough contact for Harry Kane to go down, but when you're desperate like Tottenham are, you get touched and the player is going to fall over,” the 60-year-old told BBC Sport.
"Maybe we should be more like Tottenham - we stay on our feet. They're so lucky today.”
Former Middlesbrough and Sheffield United forward Jan Aage Fjortoft, who now works as a Bundesliga expert, was also not impressed with the penalty decision and took a dig at a common perception in the Premier League.
You have to call that a "cheap" penalty... But English players never dive......so Tottenham - West Ham 2-2— Jan Aage Fjortoft (@JanAageFjortoft) February 22, 2015
The decision over Kane’s penalty will be debated for days to come, but the fact is that it cannot be overturned.
The draw at White Hart Lane on Sunday means that Tottenham are now seventh in the Premier League table with 44 points from 26 matches, just three points behind fourth-placed Manchester United.
Meanwhile, West Ham are currently eighth in the standings with 39 points.