Green-Tregaro competed in Thursday's qualifying round of the high jump at Luzhniki Stadium with her fingernails painted in the colours of the rainbow flag used by the gay movement.
Meanwhile, American 800 metres runner Nick Symmonds said he was shocked by Isinbayeva's comments and that he had been told he risked jail if he wore a rainbow badge.
"It's disrespectful to our country, disrespectful to our citizens because we are Russians," Isinbayeva, speaking hesitantly in English, told a news conference.
"Maybe we are different than European people and people from different lands. We have our law which everyone has to respect. When we go to different countries, we try to follow their rules. We are not trying to set our rules over there. We are just trying to be respectful.
"We consider ourselves, like normal, standard people, we just live boys with women, girls with boys... it comes from the history.
"I hope the problem won't ruin our Olympic Games in Sochi ," added the 31-year-old, who is one of Russia's best known athletes and won her third world title in front of an enthralled crowd on Tuesday.
The controversial Russian legislation, which was passed in June, outlaws some aspects of the promotion of homosexuality and has become a political hot potato ahead of next year's Sochi Winter Olympics, when it will apply to athletes and spectators.
Critics of the law have said it effectively disallows all gay rights rallies and could be used to prosecute anyone voicing support for homosexuals.
Last week, the International Olympic Committee (IOC) said it had sought clarification from Russia on how the law would be applied while there have already been some calls for a boycott of the Games.
Isinbayeva, who is an ambassador for Sochi 2014 and will be mayor of the main athletes' Olympic village, was against this.
"Of course, I don't support this boycott," she said. "I'm also against this polemic and feel sorry that they try to involve the athletes in such a problem... because we are not prohibiting athletes from participating in Sochi even if they have no traditional relationships," added the world record holder.
"It doesn't matter because... we don't care about nations, about different skin colours, we are athletes, we are one family, and we work very hard for only one goal, to take a gold medal in an Olympic Games, to participate in an Olympic Games.
"We are against publicity but not of course against every choice of every single person, it's their life, its their choice, it's their feelings but we are against the publicity in our country and I support our government," she added.
Symmonds, the only athlete to speak out against the ban in the build-up to the world championships where he won a silver medal, voiced his concerns again on Thursday.
"It blows my mind that a young, so well-educated woman can be so behind with the times," Symmonds told BBC Radio 5 Live.
"Guess what Yelena, a large portion of your citizenship are normal, standard homosexuals.
"I wanted to compete with a rainbow sticker but was told I would go to prison if I did that.
"It was suggested that if I pushed this too far it was a real possibility."
Asked what the feeling about the law was among the athletes in Moscow, Symmonds said: "It's a very divided subject but from most of what I've seen, this is not an issue for my generation. We believe in equality.
"There's been a huge shift to equality now being the majority view in America. Here it seems the majority of people respect this law so you have to respect that in a democracy.
"But if you are going to host the Sochi Olympics, history will look back and say 'you are on the wrong side of history, Russia'."
Symmonds said he was against a boycott of Sochi but would continue to speak out.
"My aim was to come here and race and try to win a medal for the United States," he said.
"Having done that, if I can help to advance the cause then that's something I'd like to do."
Green-Tregaro got the inspiration for her discreet display of support from seeing a rainbow over the Russian capital.
"When I first came to Moscow, the first thing I saw when I opened the curtains was a rainbow over Moscow and I thought that was a pretty good sign," the 2005 world bronze medallist said.
"I hadn't thought about it before, then I decided to paint my nails. I usually do my nails in something that feels good for me and it was a simple way of showing what I think."
"It felt right," she said showing her brightly coloured nails painted in red, yellow, gold, blue and purple.