The Foxes right-back was given a second yellow card in the 54th minute for pulling back Olivier Giroud on the left wing as the Frenchman attempted to make an attacking run.
Simpson had earlier been booked for body-blocking Alexis Sanchez but the second booking was very questionable and ultimately cost Leicester the match as Arsenal scored their two goals after the visitors were reduced to ten men.
The defeat sees Leicester's lead at the top of the Premier League table cut to two points with Tottenham Hotspur and the Gunners now within striking distance, which has Ranieri feeling poorly about the unfortunate defeat in North London.
"My reaction is to laugh with you because I am strong and I want my players to follow me," said the Italian.
"If I think about the match I am very angry because I think maybe I make mistakes but an international referee gives two yellow cards for normal fouls and the match was full of fouls.
"I remember the first half when we scored and there was a bad tackle from Aaron Ramsey and it was a yellow card but it is not the same yellow card when Simpson stopped the other player.
"Maybe (he sent Simpson off) because the crowd pushed a lot and put him under pressure. But I am very proud of my players. They showed a fantastic performance.
"Also sometimes the referee stopped the time at 94 (minutes) - four minutes' extra time. But there were five minutes' extra time when they scored. Sometimes they stopped when it was a corner or a free-kick, finished. But it's okay. It doesn't matter.
"We continue to fight."