Kanu scored a last-gasp goal to secure a hard-fought three points for the Gunners but it was all too much for the Bolton boss.
"This is the second week running that we've been beaten in the final minute," said Allardyce after the match.
"The players are distraught after a magnificent effort."
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He said: "I was very disappointed in the major decisions made by the referee, but I also had to shove Ivan out of the way or I might have strangled him!
"We would have held on if we had kept 11 men on the pitch. So, in many ways, losing the game is our own fault and in particular Ivan's for getting sent off for such a petty thing.
"He threw the ball to our keeper. As always, the referees will say that's a bookable offence and they have to do it."