Ian Poulter led the criticism of the Muirfield course after scoring during the first round proved increasingly tough in hot conditions that continued to harden, and quicken, the fairways and greens.
Yet 1998 champion O'Meara, 56, made light of the difficulties to card five birdies and an eagle in a four-under-par 67.
And he was not the only old stager to impress with Miguel Angel Jimenez (49), Tom Lehman (54) and Todd Hamilton (47) – the latter two also former champions – all under par.
O'Meara (pictured) said: "I'm not saying that I haven't complained or gotten upset on the golf course, but I'm not a big fan of guys that get out there and whine a lot.
"I just don't see any reason for it, especially today's generation.
"They're so talented, the players today and they're playing for so much money.
"To be at the top level of whatever sport you're in, that requires some responsibility.
"That aspect of it I think players should be more aware of and players need to hopefully conduct themselves in the right manner on the golf course.
"When they don't, it does bother me to be honest."
O'Meara, whose British Open triumph came at Birkdale in a glorious year in which he also won the US Masters, did not have any particular complaints about the course and felt his experience had been crucial.
The American, playing in his 28th British Open, said: "I've seen the most horrendous conditions you can think about playing golf in.
"I've stood on holes where I could barely hold on to the club and it's freezing, raining, sleeting.
"To me that's way more miserable than what we had out there. I thought it was tough, it was challenging, but unfair? I say no."
O'Meara now returns refreshed for his second round and put himself further into contention for a third major title.
He said: "Do I think I can (win)? When I play like I did today, yeah, I think I can."