"Ugandans know they are moving away from donor dependency," government spokesperson Ofwono Opondo told AFP on Friday.
"We cannot compel the Americans to give us their money. Ugandans must be ready and we are rightly doing so, paying our bills. We need to be frugal."
In the steps unveiled on Thursday, specific Ugandan officials involved in "human rights abuses" - including against the gay community - will be barred entry to the US, National Security Council spokesperson Caitlin Hayden said.
Signed by President Yoweri Museveni in February, the law calls for "repeat homosexuals" to be jailed for life, outlaws the promotion of homosexuality and obliges Ugandans to denounce gays to the authorities.
The legislation "runs counter to universal human rights and complicates our bilateral relationship", the White House said, renewing calls for the law to be repealed.
US Secretary of State John Kerry has likened the Ugandan law to anti-Semitic legislation in Nazi Germany.
Sanctions include cancelling a military air exercise, imposing visa bans and freezing some aid.
Surge in human rights violations
Rights groups say the law has triggered a sharp increase in arrests and assaults of country's lesbian, gay, bisexual and transgender (LGBT) community.
Human Rights Watch (HRW) and Amnesty International said in a joint report last month the LGBT community had faced a "surge in human rights violations", with people being arrested, evicted or losing their jobs, and at least one transgender person has been murdered since the law was passed.
But the government dismissed the reports, claiming not to have received a "single report about a gay person being intimidated or harassed."
"About the sanctions of Ugandan officials who allegedly intimidate lesbians and gay people, let them [Americans] not be cowards and come out and share the information of those involved, and the law take its course," Opondo said.
"We are surprised that a foreign government is the one reporting these alleged abuses, yet we have not received these complaints."
Opondo said Uganda would cope, adding "we have been able to fund our budget up to 82%".
"We don't think it is critical for Ugandans to travel to America or any other country," he said.
"With modern cyber-technology we can comfortably conduct business from the comfort of our offices."