Henderson, who directed eradication of small pox under the World Health Organization, said people should be open about the "threat" of H1N1.
"What our colleagues must keep in mind that there is a need to be open and frank with the public at all times," he said. "Some would like to have the threat of 'continuing pandemic' on the label as an encouragement for more people to get vaccinated. Not a good idea."
Looking forward, most U.S. doctors agree that the H1N1 has fizzled out. But some doctors feel that the public underestimated the potential threat of H1N1 virus last year.
"We should be careful not to blame the government for over exaggeration of risk. They did exactly what they were supposed to do and did it reasonably well," said Dr. Peter Katona, of the David Geffen School of Medicine at the University of California Los Angeles.
"There was a lot to learn. This will happen again and we will need to be prepared - maybe even more prepared - the next time," said Katona, who previously worked for the CDC.
Dr. William Schaffner, chairman of preventive medicine at Vanderbilt University, has already begun to hear questions about how H1N1 will affect next year's seasonal flu shot.
"Patients will be asking 'if I got the H1N1 last year, do I need to get the vaccine this year?' or 'Gee, I thought I was sick with H1N1 last year, should I get the vaccine this year?'" said Schaffner. "The answer is yes."
However this year, the seasonal flu vaccine will include protection against H1N1 and, for the first time, the CDC's Advisory Committee on Immunization Practices will recommend everyone over age 6 months be vaccinated for the flu.
Previously the committee only recommended children age 6 months to 18 years, and people in contact with others with a "high risk" group receive the vaccine.
"We're not still in a pandemic mode," said Schaffner, who added it was "luck" that many of the elderly had built up immunity to a virus similar to H1N1 in the 1950s.
"Some of the protection we got from our infection back then carried over this past year," said Schaffner. "If we had not had that kind of protection, I can assure you that it would have been a very grim flu season."
The Associated Press contributed to this story