The Whites confirmed on their Twitter account that an appeal will be lodged tomorrow morning.
Berardi was sent off after 14 minutes at The Den on Saturday, referee James Linington deciding the defender had not only fouled Tom Bradshaw in the box, but denied a goalscoring opportunity without making an attempt to play the ball.
Replays appear to suggest there was little if any contact between the players and Leeds are also likely to point to Kalvin Phillips' proximity to the striker as he hit the turf.
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Jed Wallace fired home the spot-kick and 10-man Leeds went on to lose 2-1, despite dominating possession.
READ: Leeds owner Andrea Radrizzani Tweeted his disappointment at 'wrong decisions' after the game.Whites boss Marcelo Bielsa refused to criticise the referee after the game but did highlight three important decisions in the game, including a Leeds penalty appeal of their own when Jack Harrison went down in the Millwall box.