The 'Lawless' actor recently used Twitter to leak a string of private emails relating to his departure from the new Broadway production of 'Orphans', which he was due to star in with Alec.
His would-be co-star has now claimed Shia is in no position to talk about the theatre as he isn't a true stage actor and has accused him of not being able to cope with the challenges of the art form.
Referring to one of Shia's tweets which read "The theatre belongs not to the great but to the brash", Alec told website Vulture: "I can tell you that, in all honesty, I don't think he's in a good position to be giving interpretations of what the theatre is and what the theatre isn't.
"I mean, he was never in the theatre. He came into a rehearsal room for six or seven days.
"There are people who are film actors who have a great legacy in the theatre. Some of the greatest movie stars had really serious theatre careers and still do. And many film actors, though, who are purely film actors, they're kind of like celebrity chefs, you know what I mean? You hand them the ingredients, and they whip it up, and they cook it, and they put it on a plate, and they want a round of applause."
Further suggesting that Shia didn't have the talent to make it on stage, Alec claims actors who are successful in front of a live audience are able to nurture a story in a way that is the "opposite of film acting".
In what seems to be a final swipe, the 54-year-old actor insisted he isn't interested in the opinion of Shia, now the 26-year-old heartthrob has decided the theatre isn't for him.
The '30 Rock' star said: "There are people who decide that's just not their thing. So for those people who I think it's not their thing, I'm not really interested in their opinion of it. But thanks."
During his Twitter spree last month, 'Transformers' star Shia posted the email he sent Alec, which was entitled "apology" and read: "A man can tell you he was wrong ... He can apologise, even if sometimes its just to put an end to the bickering. Alec, I'm sorry for my part of a disagreeable situation (sic)."
Alec's response read: "I've been through this before. It's been a while. And perhaps some of the particulars are different. But it comes down to the fact that what we all do now is critical. Perhaps especially for you.
"I don't have an unkind word to say about you. You have my word."
Shia has now been replaced by Ben Foster in 'Orphans' - which tells the tale of two orphaned brothers who grow to regard a gangster they attempt to kidnap as a father figure.