Catherine Brown said that testing was the right way to address the issue, and said the focus would be on areas of higher risk.
But she admitted that how many people who had unknowingly eaten horse meat was likely to be impossible to ascertain.
"I don't think that we ever will (know how many), because these tests are a snapshot, so even where we find things it is very hard to work out how long, what number of batches, so I think it is unlikely that we will ever know that. It is shocking," she told the BBC.
Her comments came as the head of a major UK supermarket chain insisted that the horse meat scandal was not "the tip of an iceberg".
Justin King, chief executive of Sainsbury's told BBC's Newsnight programme that supermarkets had not been slow to react to the scandal, but conceded there was a long way to go before the food industry could fully explain how the crisis has come about.
He said last night: "I don't think it's the tip of an iceberg. I think there are some encouraging signs from today's tests that we are starting to get to the bottom of this particular issue.
"We, in Sainsbury's, have a huge testing programme - we have 50-odd people, whose full-time jobs are to test product.
"They test raw materials when they come into the factory. The product is delivered to our warehouses and we buy product, as customers do, to test it too. And most of the industry would say something similar.
"So, we go to great lengths to ensure our food is what we expect it to be. Trust is the core of our businesses."
Officials investigating the horse meat mis-labelling scandal will continue examining evidence today after three more plants were raided.
The FSA visited two premises in Tottenham, London and one in Hull, Yorkshire, on Thursday.
Investigators, accompanied by police officers and local authority officials, made seizures at the three sites and removed meat samples for testing.
An FSA statement said: "Computers and documentary evidence have been removed from these premises, as well as meat samples that have been taken for testing."
The FSA also said it had passed on evidence to Europol - the European Union's law enforcement agency and the authorities in dozens of countries.
It said: "The FSA has submitted a full file and evidence on this issue to Europol.
"The agency has continued to provide information to Europol, and this information has now been analysed by both Europol and law enforcement agencies in 35 countries - across Europe and elsewhere."
One of the plants raided in north London, Dinos & Sons Continental Foods, said it was "co-operating with local trading standards officers and the FSA".
Bosses at the plant, which is based in the Millmead Industrial Estate in Tottenham, issued a statement saying: "Dinos & Sons Continental Foods Limited confirms that it is co-operating with local Trading Standards Officers and the FSA in respect of all its current investigations.
"Dinos & Sons has been asked to clarify its position in respect of the transportation and storage of frozen beef that was imported by, and belonged to, a third party that the FSA is investigating.
"Dinos & Sons did not keep this frozen beef in the same premises as its own products and there was therefore no possibility of any cross-contamination.
"At no time has Dinos & Sons produced or manufactured anything that is under investigation or is the subject of any possible contamination or mislabelling.
"There is no suggestion whatsoever that Dinos & Sons manufacturing processes have been compromised in any way. Tests undertaken by independent laboratories on Dinos & Sons products have proved negative to date for any contaminants, including horse meat."
A second company was named as being Flexi Foods Ltd, in Hull, which stored meat at Dinos & Sons Continental Foods, it was reported.
Flexi Foods was the supplier of 60 tons of beef that was contaminated with horse meat and sent to Ireland for processing, the Daily Telegraph said.
A spokesman for Flexi Foods told the newspaper: "We are aware of an ongoing, wide-ranging, Food Standard Agency investigation. We have been asked to supply some information in relation to only one part of this investigation, with which we are quite voluntarily co-operating.
"We feel it would not be fair, nor appropriate, to comment any further whilst the authorities continue with their much wider investigations."
The raids came as three men who were arrested on Thursday remain in police custody on suspicion of offences under the Fraud Act.
Dafydd Raw-Rees, 64, the owner of Farmbox Meats near Aberystwyth, and a 42-year-old man were arrested in Wales.
A 63-year-old man was also arrested on suspicion of the same offence at Peter Boddy Slaughterhouse in Todmorden, West Yorkshire.
Both plants were inspected on Tuesday by the FSA.
Yesterday, the FSA released eagerly awaited test results for possible horse meat contamination.
The watchdog said 2,501 tests were conducted on beef products, with 29 results positive for undeclared horse meat at or above 1%.
The 29 results related to seven different products, which have already been reported and withdrawn from sale.
The products linked to the positive results were confirmed as Aldi's special frozen beef lasagne and special frozen spaghetti bolognese, the Co-op's frozen quarter pounder burgers, Findus beef lasagne, Rangeland's catering burger products, and Tesco value frozen burgers and value spaghetti bolognese.
As the results were confirmed, pub and hotel group Whitbread became the latest company to admit horse DNA had been found in its food, saying their meat lasagnes and beefburgers had been affected.
The firm, which owns Premier Inn, Beefeater Grill and Brewers Fayre, said the products had been removed from their menus and will not be replaced until further testing has been carried out.
Horse meat was discovered in school dinners for the first time since the scandal began, it was also revealed.
Cottage pie testing positive for horse DNA was sent to 47 Lancashire schools before being withdrawn.
Judy Hargadon, chief executive of the Children's Food Trust, said that parents, schools and caterers in Lancashire would feel "let down".
"Whether you're a parent buying food at the supermarket or a caterer dealing with a supplier, we're all buying our food in good faith," she said.
"What the last few weeks have taught us, here in the UK and elsewhere, is that people buying in good faith have all been let down by these issues in the supply chain.
"It's important that parents don't panic - listen to the advice of the Food Standards Agency and talk to your school as they will be able to reassure you about any steps they and their caterers are taking."