Carlisle saw red after just seven minutes for a late challenge on Theo Robinson but Laws was quick to defend the centre-half.
He said: "It wasn't a sending off. I thought it was very harsh.
"I don't know whether the referee has been given a message to stamp down on any challenges whatsoever, but the first five minutes? Clarke's clearly not caught the player and his challenge was low.
"We've got to take a stern look at it and if we make the decision to go with the appeal then we've got to go with it.
"Maybe we take the risk but I don't want to lose him for four games."
The Clarets responded well to the early setback and took the lead through Jay Rodriguez's header before Scott Barron levelled with a low drive.
Laws was pleased with his side's efforts after playing with a man short for so long and hailed his makeshift defence.
He said: "We've had to rise above the red card. Andre Bikey looks like he could have done some damage to his ribs so 10 minutes into the game our two centre halves have come off which was a worry but great credit to the team.
"It was frantic at times but with 10 men for over 80 minutes, it's incredible. We put a lot of effort in and showed a lot of discipline so we deserved what we got.
"The fact that we've drawn the game is a little disappointing because I would have loved to have played the game with 11 men. Their equaliser was disappointing because we gave them that opportunity - we should have put the ball into row Z.
"But all credit to our lads for responding in the right manner. They've put some great effort in and I thought they were outstanding."
Millwall manager Kenny Jackett felt that Carlisle had to go and rued his side's poor finishing in the draw.
He said: "Carlisle's mis-timed the tackle. There was another on Tony Craig as well and he's had two lots of stitches in his shin.
"Tony was lucky and that could easily have been a red.
"There's a considerable amount of frustration for me. We had the chances to win the game and built up the momentum and pressure against their 10 men.
"The only criticism I can have against my players was their finishing. The woodwork has come to their rescue once or twice but there was a winning performance there.
"We had a number of chances and that's something we have to look at because we could have finished Burnley off. Sometimes you have to earn your luck but that type of performance is very encouraging for me as a manager. There was plenty of passion and tempo."