A member of staff in the council's finance department inputted the wrong fire and police precepts, with the result that residents were under-billed by between 2p and 10p for the year.
The cost of not collecting the shortfall would have been£7,000, but the council's legal advice was that failure to rebill would place Croydon in breach of council tax regulations.
In a further embarrassment, the council had to reprint bills and then amend them by hand because its computer package would not allow for another billing to take place.
Croydon finance and IT director Peter Leeming said: 'It is the first time in my 20 years as a local government finance director that I have ever encountered something like this. I am very sorry and embarrassed that it has occurred here in Croydon.'
Mr Leeming wrote to all residents over the weekend to explain about and apologise for the error.
He told them: 'You may well be concerned as to why the council has gone to the trouble and expense of sending out a new demand when the sum involved is so small. Naturally, we would have much preferred to have overlooked this tiny reduction in your original demand.'
The council has now tightened up procedures, so that in future all council tax figures will have to be 'double signed', with Mr Leeming as one of the signatories.