But he feels the turnaround with tennis gives hope for golf
The president of the International Golf Federation thinks a number of players are over-reacting in their decision not to go to the Olympics.
All of the world's Top Four golfers - Jason Day, Rory McIlroy, Jordan Spieth and Dustin Johnson - have pulled out from competing at next month's Games in Rio due to concerns over the Zika virus.
There have been suggestions in some quarters that the health fears are being used as an excuse, as other sports do not have such a level of withdrawals.
"There is no doubt that the number of withdrawals hasn't shown golf in the best light and we have to accept that. But we do understand why these individual decisions have been taken. Personally, I think there's been something of an overreaction to the Zika situation, but that's for individuals to determine," said Dawson.
But Peter Dawson says they can be encouraged by what happened in tennis.
"It’s worth remembering the tennis experience when they came back into the Olympics in, 1988. They had a lot of difficulty attracting the top players, and just look at it now. It is a very significant Olympic sport and very well supported by the top players. I think golf will take a little bit of time as well. But I don't think it will take that long."