Dawson said the R&A hopes to introduce drug testing for 2009
Plans for the Open to become the first major to test for drugs have been abandoned by the tournament organisers.
Testing is expected to start on the European and American tours in July, but the Royal and Ancient Club (R&A) said the Open will now start in 2009.
It took the decision because some qualifiers take place in countries which do not have the same education programme as Europe and America.
R&A chief Peter Dawson said the delay was "slightly unsatisfactory".
Dawson was one of the driving forces behind the formation of the anti-doping policy adopted by the professional game late last year.
We're dreaming if we think it (drug use) is not going to come into golf
"We played a leading role in the development of a policy of which we are very proud," said the R&A's chief executive.
"But it is very important that players understand what it is about and given that quite a number of players do not play on the PGA or European Tours we decided that it will not start at the Open this year.
"But we very much hope and intend to start next year. If the Open was in October we would probably be drug-testing this year.
"I think we have a pretty good record at taking the lead in drug-testing. We made a big contribution towards its introduction and I think our record in this area stands scrutiny."
On the eve of last year's championship at Carnoustie, three-time winner Gary Player hit the headlines with claims that a number of players were taking performance-enhancing substances.
"I know for a fact that some golfers are doing it," said the South African. "And the greatest thing that the R&A, the USGA and the PGA can do is have tests at random - it's absolutely essential that we do that.
"We're dreaming if we think it's not going to come into golf."