Media playback is not supported on this device
Professor Andrew Pipe has left his role as chairman of the body's doping control review board, as have two other members of the eight-strong panel.
Seven swimmers competed despite bans from the board for doping violations.
Fina said it gave the advice to the International Olympic Committee and the Court of Arbitration for Sport.
The federation added it was not responsible for the final outcome.
Those banned by the board included Yulia Efimova, one of 37 Russian swimmers at Rio, who won two silver medals in the women's 100m and 200m breaststroke events.
She was banned initially by the International Olympic Committee (IOC) because of two failed drug tests.
Each sport's governing body had to determine whether Russian athletes linked with past doping offences or state-sponsored doping were eligible for Rio 2016, after the IOC decided against a blanket ban in the wake of a World Anti-Doping Agency investigation.
Pipe, the chairman of Fina's independent doping control review board (DCRB),and two of his colleagues stepped down this week.
In a letter to the governing body, the experts added that "the failure of Fina to enact other recommendations that the DCRB has made in the past, is incompatible with our dedication to clean sport and optimal anti-doping practice."
Fina president Dr Julio C Maglione said: "Fina always co-ordinates with all stakeholders in the sport movement to assure that transparency and zero tolerance in the fight against doping is in place, thus protecting the clean athletes.
"Please rest assured that we will continue the same policy in fighting against doping without any limitation, equally applying the doping control rules to all athletes and all Fina Member Federations."
Three anti-doping advisers to Fina have resigned, saying swimming's world governing body ignored a call to ban some Russian athletes from Rio 2016.