The council mistakenly sent the list of children, including personal information, to a number of its in-house foster carers. It has now launched an investigation into the data breach and insisted that 'no children were put at risk'.
But County Councillor George Adamson, who is also the leader of Cannock Chase District Council, described the incident as 'totally unacceptable' and described the county council as a 'shambles'.
He said: "This is serious and totally unacceptable. It is a big worry.
"How an earth have they managed it? They say they have not put children at risk but how do they know that?
"It is personal information they have put into the public domain. There needs to be an investigation.
"It is a complete shambles and indicative of how the county council is being run at the moment."
West Midlands MEP Bill Etheridge described the breach as a 'very serious error' and called for changes to be made to make sure this mistake is not repeated in the future.
He said: "This is a very serious error which could have risked the safety of vulnerable children.
"An apology is only the start of what is required.
"The council should undertake a full review of what happened and make changes to ensure this can never happen again in the future."
Staffordshire County Council has apologised for making the mistake and has insisted it is taking the matter 'very seriously'.
In a statement Mark Sutton, the council's cabinet member for children and young people, said: "We can confirm that a number of our in-house foster carers where sent an email with a list of children in our care in error.
"Whilst the information was confidential, it only contained basic personal information and at no time were children put at risk.
"All of our foster carers sign a confidentiality agreement in relation to the sensitive information they receive in the course of their fostering activities and are used to dealing with such information in a confidential manner.
"We do take these matters very seriously and are carrying out an investigation to understand what happened and if any action is required to prevent it from happening again in the future."