Reid, 28, has made just two Carling Cup appearances in nearly a year after sustaining a serious knee injury and saw his first-team comeback hindered recently with a niggling Achilles tendon complaint.
When asked about the player, Trapattoni cast doubt on whether he would ever be able to return to his best, saying a full recovery would be "very, very difficult", something which Reid himself declared his surprise at.
Allardyce, though, pulled no punches with his response on the matter, demanding action from both the Football Association of Ireland and Trapattoni himself.
"It's disgraceful, completely out of order," said the Rovers boss, whose side face Chelsea in Saturday's late kick-off.
"He's not talking correctly in terms of Steven's injury. What he is saying is completely untrue and something he should apologise for.
"He has undermined us as a football club, undermined Steven as a player and he has really been very, very naughty in what he has said.
"He should make a public apology and hopefully that will be the end of it.
"Steven has had a long haul and he's trying to resurrect his career and secure a new contract. He also wants to go and play for his country as he has done many, many times and given his all on every occasion.
"There's no player more honest than Steven and to be dealt that sort of a blow at this stage, when he's not feeling the best, trying to come back from a big injury and picking up another little niggle, is very, very disrespectful to say the least. It's disgusting."
For his own part, former Millwall player Reid confessed to be being "amazed" at Trapattoni's diagnosis, but insisted he was desperate to play for the veteran coach in the World Cup qualifying play-off against France next month.
Allardyce commended his man for tact but insisted he would not let the matter lie.
"That's the mark of Steven for you," he continued.
"Perhaps I haven't got the same dignity as Steven. Perhaps I just speak it as I see it. Perhaps he's more sensible than me. But I'm not happy with what Trapattoni said, I'm disgusted with it.
"I think his association should bring him to task. I think we as a football club should bring him to task and make him justify what he has said, but the thing is he can't.
"I've never spoken to him and after what he's said I don't want to. Steven's had a very difficult time and the last thing he needed was to sit down and read his international manager trying to write him off."
Back on the pitch, Rovers will be looking to collect a first away point of the season in one of the hardest possible venues.
They will have to do so with Italian forward Franco Di Santo, ineligible to face his parent club, as well as Vince Grella and, possibly, full-back Pascal Chimbonda.
But Allardyce believes a shock result could yet be possible.
He said: "We haven't picked up a point away from home all season and Chelsea have only conceded once at home in the Premier League all season on the opening day of the season. If that doesn't sound like a daunting task, I don't know what does.
"But in any given game of football you can catch a team at the right time. Maybe not on their top form, maybe a little fatigued from their European efforts in midweek, maybe a few knocks. You can try to take advantage of that if your team plays their best."