Report says pyres should never be used again
He said the government had been faced with an unprecedented situation, with no warning.
Devon was one of the counties worst affected by foot-and-mouth with 173 cases confirmed and 390,000 animals slaughtered.
Monday's preliminary report from a public inquiry in Devon said there should be a national contingency plan for any future outbreak.
Lord Whitty has now admitted such a plan existed - but said it was only known to ministry staff.
The contribution arrived 11 days after a week of public hearings ended this month at County Hall in Exeter.
The report by Professor Ian Mercer, who chaired the hearings for Devon County Council, made 31 suggestions for future handling of foot-and-mouth disease.
He said the government should be "sitting round a table and sorting it out", without waiting for the results of the three national inquiries into the crisis.
Officials 'insensitive'
Lord Whitty said of the report: "Aspects of it are critical.
"It does raise issues of organisation and communication that the government has to take seriously.
"There were communication problems and insensitivities at the beginning.
"That is not criticism of our staff, but we do need to improve communication and be better prepared if this happens again."
But he said in some respects, the criticisms were too simplistic.
Lord Whitty said: "We were faced with a rapidly spreading disease that bore no relation to what went before. What I wouldn't accept is that the overall strategy was lamentable."
He said there had been a contingency plan in place but that it was "not sufficiently shared".
'Animals suffered'
The report criticised the decision not to vaccinate livestock.
But Lord Whitty said it could not have worked in the face of opposition from farmers - including those in Devon.
Vaccination in the Netherlands did not prevent large-scale culling, he said.
But he conceded: "Vaccination could, in future, be considered as a supportive mechanism."
Professor Mercer's report said huge pyres of burning dead animals in the open should never be used again.
A vet had told the inquiry that burning infected carcasses had spread the disease, and another said methods used were "medieval".
The RSPCA said animals suffered in a way that would normally lead to prosecution, and evidence was heard of bungled culls and insensitive and belligerent Defra staff.
The report says a national contingency plan should be reviewed and rehearsed at least every five years.
It also calls for:
David Hill, of the National Farmers' Union, said the slaughter had "frightened" farmers.
He told the BBC: "There's no doubt there was a very heavy-handed, almost jackboot approach to going in there and killing animals.
"It upset members at a time of their greatest trauma."
Fifty witnesses gave evidence during the hearings and there were 360 written submissions.
Professor Mercer's report has been presented early to meet a deadline for submissions to Sir Don Curry's national inquiry into the future of farming and food.