Diplomats have said the US withdrawal could bolster Cuba, Russia, Egypt and Pakistan, which resist what they see as United Nations interference in sovereign issues.
Earlier, deputy permanent representative Yu Jianhua of China - which has sporadically faced USA criticism over its human rights record - said his delegation was "disappointed" about the US pullout.
"It is bad news for everyone who cares about human rights", Slovenian President Borut Pahor said on the UNHRC floor in Geneva on Wednesday.
The United States is the first nation to voluntarily exit the council since its inception in 2006. Indeed, its decision to fully withdraw appears to be a rebuke of the council, in that it withdraws the US's ability to take a front seat in important global issues.
Elizabeth Wilde, deputy head of mission in Geneva for Australia, said her country "shares numerous U.S.'s concerns about the HRC", but will continue to support the council "despite its flaws".
"The Human Rights Council has become an exercise in shameless hypocrisy - with numerous world's worst human rights abuses going ignored, and some of the world's most serious offenders sitting on the council itself", Pompeo said.
Haley also said the "disproportionate focus and unending hostility towards Israel is clear proof that the council is motivated by political bias, not by human rights".
Slovenian ambassador Vojislav Suc, who now holds the council's rotating presidency and has been pushing a faltering reform drive, described the Geneva-based chamber as the best place to trigger action on risky rights crises.
"China expresses regret at the USA decision to withdraw from the U.N. Human Rights Council", China's foreign ministry spokesman Geng Shuang said at a briefing on Wednesday, according to the news agency.
"This decision is counterproductive to American national security and foreign policy interests and will make it more hard to advance human rights priorities and aid victims of abuse around the world", the organizations said in a joint statement. She had been threatening the pull-out since a year ago unless the council made changes advocated by the U.S. "Of course Finland is committed to the work of the Human Rights Council and based on our experiences we would have hoped that the United States would have continued that co-operation".
The Russian mission described the council as a "key worldwide platform for cooperation in protecting human rights".
Israel is the only country recorded as a dedicated agenda item.
"Look at the council membership and you see an appalling disrespect for the most basic human rights. In fact, that's why many of them run for a seat on the Human Rights Council in the first place: to protect themselves from scrutiny", Haley said. The United States was half-way through a three-year term on the Geneva-based 47-member body.
Russia's United Nations mission responded in a statement that the USA had tried but failed to turn the Council into an "obedient instrument for advancing their interests and punishing the countries it dislikes". The U.S. joined the body only in 2009 under President Barack Obama.