O'Meara, who called Singh a friend, said he heard about the Fijian's admission on Wednesday, but doesn't believe he benefited on the course from the unorthodox treatment.
"I was obviously a little bit surprised with what I heard, but I don't think Vijay is a guy that would ever take advantage of anything. I know Vijay," O'Meara said after finishing his first round at the Dubai Desert Classic.
"I guess they could probably suspend him for a couple of months. I would think so," the two-time major winner said. "Listen, people have had to pay the price before and he should be no different. If that is the case and the commissioner and tour feels he should be suspended for X amount of time, I think Vijay is man enough that he'll do that."
The 49-year-old Singh said he paid one of Sports With Alternatives To Steroids' owners $9,000 in November for the spray and other products, Sports Illustrated said. Singh released a statement at the Phoenix Open confirming he had taken it, but that he was "absolutely shocked that deer-antler spray may contain a banned substance and am angry that I have put myself in this position."
Singh, who won the last of his 56 titles in 2008, said he will co-operate with the tour's review of the issue.
Bob Charles, the 1963 British Open winner, said in New Zealand on Thursday he also used and promoted deer-antler spray for more than 20 years, and was surprised to learn it contained a banned substance. Charles was a spokesman for the deer-antler product and used it daily over two decades.
Despite Singh's admission, O'Meara and other golfers said they felt the measures in place to combat doping in golf, including random testing, were adequate.
"I don't think doping is a problem in golf whatsoever. I really don't," Paul Casey said. "There are so many facets to our sport. Why was he taking it? Was he taking it to recover from injury? It doesn't help you get the ball in the hole at the end of the day. This is the first case I've heard where a guy admitted to taking anything."
The oddity of deer-antler spray being used by golfers was the talk on the Dubai course on Thursday, with Lee Westwood among the players having a good laugh about it. Most said they had never heard of it until the story on Singh.
"Deer-antler spray? That sounds like something you wax your car with, doesn't it?" Westwood said. "I've never heard of it. ... You have to be careful about what you take. I try not to take anything now, really, other than Corona and vodka."
Colin Montgomerie, a rival of Singh during their heydays, called the whole case "odd" and said the European Tour doctor "came to us (and said) deer antler, whatever it is, don't take that this afternoon lads."
Montgomerie said the tour had nothing to worry about with him when it came to doping.
"I can only speak for myself and it's not widespread within the Montgomerie family," the 2010 Europe Ryder Cup captain said, looking down at his torso. "Unfortunately. You can see that though, can't you, really."Suggest a correction