The 24-year-old won two silver medals in Rio but was booed by spectators and criticised by her rivals after she was allowed to compete, having initially been banned by the International Olympic Committee because of two failed drug tests.
Efimova tested positive for meldonium earlier this year, but had a suspension lifted by the sport's governing body, Fina, after the World Anti-Doping Agency admitted it was unsure how long the substance - which was only banned this year - stayed in the body.
She was previously banned for 16 months after an anabolic steroid was found in her system in 2013.
At times struggling to contain her emotions, she says she "made a mistake", but only took meldonium before it was banned.
Efimova says she feels no anger towards US rival Lilly King, who said the Russian should not have been allowed to compete in Rio.