The flags of Iraq and Afghanistan appear in a commercial as part of Bush's drive for re-election in November. A narrator says: "At this Olympics there will be two more free nations -- and two fewer terrorist regimes."
But coach Adnan Hamad said Iraq, still plagued by violence daily, remained a country under occupation.
"You cannot speak about a team that represents freedom. We do not have freedom in Iraq, we have an occupying force. This is one of our most miserable times," he said.
"Freedom is just a word for the media. We are living in hard times, under occupation."
The Iraqi men's soccer side has been one of the surprises of the Olympics, reaching the semifinals of the competition. They play Paraguay on Tuesday for a place in the final.
But their success has been overshadowed in the past few days by rows over the commercial for Bush, who went to war and ousted Iraq's Saddam Hussein last year.
Although Washington has officially handed power to an Iraqi interim government, more than 130,000 American soldiers remain in the country, battling with insurgents from various factions. Western officials also hold key positions behind the scenes.
"We want to give our people a cause to celebrate, to forget their problems," Hamad told reporters in the northern Greek city of Thessaloniki, the venue for Tuesday's match.
After Sports Illustrated magazine quoted Iraqi team members expressing outrage at the Bush ad, a British adviser to the Iraqi Olympic committee accused journalists of taking advantage of players' naivete and said sport should not be politicised.
But Hamad said: "One cannot separate politics and sport because of the situation in the country right now."
He said the violence which continues to afflict Iraq, more than a year after Bush declared major combat there was over, meant the team could not fully enjoy its success.
"To be honest with you, even our happiness at winning is not happiness because we are worried about the problems in Iraq, all the daily problems that our people face back home, so to tell you the truth, we are not really happy," he said.
The International Olympic Committee said it had not been in touch with the Bush campaign about its use of the Games in the commercial. National Olympic committees own the rights to the Olympic name and symbols in their countries, a spokeswoman said.