Stunned teachers were able to read the names of other teachers who had also been refused a job, which included the email addresses of all 48 rejected candidates.
Many of those affected were furious, not only at the impersonal way they received the news, but also because the move is claimed to have breached data protection rules in disclosing others' email addresses.
Gary Greenhorn, head of educational resources at Falkirk Council, said: "We recognise that this was an error on our part and we apologise to all the unsuccessful candidates for any upset caused.
"A technical error in our email system was at fault, and we have taken steps to ensure that this does not happen again. We have apologised in writing to all of the candidates concerned."
The EIS said candidates should never have been told in such a way, and union representatives plan to raise it with the local negotiating committee for teachers after the Easter break.
A source close to the situation described the incident as "shoddy practice"
and said a letter of apology from the member of staff at Falkirk responsible was not enough. "She has still breached the data protection legislation. I have spoken to data protection officials, and they have told me it is a clear breach of that act," he said.
"This is crass ineptitude. The person that did this must be disciplined because it is a very poor way to treat people."
The council declined to say whether disciplinary proceedings or an investigation were underway.