Ferguson was sent off in injury time for two bookable offences and will now miss the game at Liverpool on Monday week.
The former Scotland international picked up his second booking when blocking an attempted throw by Pablo Zabaleta.
McLeish said: "Barry came in and said he was daft. He knows we will miss him at Anfield and it will cost the team with us having such a fragile squad.
"We can't afford to lose players through a silly act of indiscipline."