Fifty-three quota places had been due to be available at the World Olympic Qualifier in Paris in June, but the IOC Boxing Task Force - organising the Tokyo 2020 tournament and the qualification events after AIBA's recognition was suspended by the IOC - scrapped the competition earlier this month because of the coronavirus pandemic.
These places at Tokyo 2020 will instead be assigned based on rankings, with the best-ranked boxer per region, per weight category receiving a berth.
AIBA revealed its concern about the decision in a statement, claiming it would still be possible to hold a qualifying tournament despite the challenges posed by the COVID-19 pandemic.
"We respect the decision of colleagues from the IOC Taskforce; it is important for us to find boxing in the Olympic programme and fulfil the Olympic dream of our athletes," the statement said.
"However, we believe that it was possible to retain the qualifiers.
"In this challenging time, AIBA strives to host as many tournaments as possible in compliance with all safety measures.
"Our experience and the experience of our National Federations suggest that it is possible to successfully conduct official competitions during the pandemic, and we would be ready to share this experience."
The IOC Boxing Task Force said the changes to the qualification system would ensure athletes from all regions have an equal chance to qualify for the Games, but AIBA claimed it would be unfair on young boxers.
"The ranking system, compiled on the basis of key tournaments of past years, does not take into account youth competitions, so young boxers born in 2001-2002 will be deprived of the chance to compete at the Games and fulfil their dream," AIBA said.
"A qualification tournament would be a more objective way to qualify for the Olympics.
"The situation with the division of quotas by continent is fair and democratic only in theory, however, in practice, it is not so unequivocally.
"All this will greatly reduce the entertainment of the Games and their value in the eyes of the fans."
AIBA also criticised the postponement of the European qualifier from April to June.
The original European event, at London 2012 venue the Copper Box, was called off after three days of competition last March because of the escalating coronavirus crisis.
The Boxing Task Force confirmed earlier this month that London would no longer host the event.
"The postponement of the European qualifiers dates from April to June may negatively affect the training cycles of athletes," the governing body said.
"Boxers, who have been left in limbo for a year, will again not be able to build their training process in the best way.
"And this will affect the quality of the participants in the Olympic tournament, which is supposed to be composed of best of the best."
AIBA was suspended by the IOC as the Olympic governing body for boxing in 2019.
It was stripped of any involvement in the boxing tournament at Tokyo 2020 because of concerns over its governance, finances and refereeing and judging.
AIBA has reiterated its offer to work with the IOC Boxing Task Force to ensure the Olympic qualifying events could take place.
"We believe that everyone should have an equal chance to prove themselves in the ring and earn the coveted ticket to key competitions," AIBA said.
"The boxing community is asking the IOC Taskforce to find a way to keep the dates of the European qualifiers and not to cancel the World Qualifiers.
"We would like to emphasise that AIBA is open to dialogue, ready to provide any assistance to colleagues in organising boxing competitions.
"The well-being of our athletes and coaches is an absolute priority for us."
The Americas qualifier is still scheduled to take place in Argentinian capital Buenos Aires from May 10 to 16.
An Asia-Oceania qualifier was held in Jordan last year, while Senegal hosted the African event.
The pandemic forced the postponement of Tokyo 2020, with the Olympics now scheduled for July 23 to August 8 and the Paralympics set to run from August 24 to September 5.