Top-ranking officials decried the decision as a "poor signal", while others demanded the resignation of the International Olympic Committee's chief Thomas Bach, a German.
"We want to tell Bach: game over, you may leave," said Ines Geipel, a former sprinter who now heads an association to help the thousands of ex-athletes involved in the former East German state's doping programme.
"The consistently cowardly manner in which the IOC deals with Russia is no more than pure cynicism," she charged, adding that "lies and cover-ups are becoming the norm while the Olympic charter and good sense is being turned into laughing stocks."
A board member of Germany's National Anti-Doping Agency, Lars Mortsiefer, also had strong words for the IOC, saying its decision "sends a poor signal for clean and fair sports".
German athletics federation chief Clemens Prokop said the IOC had done "serious damage to its credibility".
Given that the Russian drug abuse was state-orchestrated, "there should have been a decision against the system, and not against individuals," said Prokop.
Anti-doping specialist Fritz Soergel meanwhile called it "a victory for Bach but not for honest sports".
There were similar howls of derision in Britain, where many had called for a blanket ban on Russia in Rio.
Bach and the IOC had resisted that in the troubled build-up to the Games.
The Guardian quoted Professor Richard McLaren, whose explosive report blew the Russian doping programme wide open last month, as accusing the IOC and Bach of badly misrepresenting his findings.
McLaren, who was commissioned by the World Anti-Doping Agency (WADA) to investigate the claims of a Russian whistleblower, said his findings were never intended to prove individual doping cases.
And he said that the broader anti-doping drive had become "political and hysterical".
Many British newspapers also took aim at the IOC, Bach, Russia and its President Vladimir Putin.
The Sun tabloid said it would publish "The real medal table" daily -- which would not include any Russian medals or any previous drugs cheats.
"Sunsport believes the Olympics should stand for integrity and sporting ideals," it thundered.
"The IOC backed away from banning Russia over the scandalous drugs cover-up that shamed sport and the country.
"But we are not scared of Vladimir Putin, or anyone else."
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