Smith picked up a plastic bottle and hurled it back into the Elland Road crowd, hitting the sister of one of his best friends.
After the hearing, in which Smith was represented by acting chairman Trevor Birch, club secretary Ian Silvester and a solicitor, Leeds made their feelings known via a terse statement.
It read: "The club are disappointed, as is Alan. Leeds United feel the player has been very harshly treated over the whole matter."
The ban covers the matches on January 31st against Middlesbrough and February 7th against Aston Villa.
Eddie Gray urged Smith to learn the lessons from his suspension-hit past and control his temperament.
"Alan knows what's expected of him no matter what position he plays in," insisted caretaker boss Gray.
"He is a vital member of our squad and the one thing we can do without is him being suspended, so in my opinion, he still has to control his temperament even better.
"He has to realise that himself because let's be fair, in football, you don't get a bad-boy image for nothing. So he has to learn to control his natural aggression, which he is working hard at. There's nothing he can't sort out.
"If that happens then he is a great asset to Leeds United, although like everybody else he is disappointed by the position the club is in. You expect that from somebody like Alan.
"But he has to react in a positive manner and make sure he controls his emotions and gets on with the job of helping Leeds United climb the table, and I'm sure he will.
"There've been a lot of players throughout the years who learn through experience, with Billy Bremner one of those players," added Gray.
"Billy learned to control his natural aggression the longer he played, and that will happen to Alan. David Batty was also quite similar when he was younger as well."