Onana failed an out of competition doping test in October last year after Furosemide was found in his urine.
In a statement posted on Twitter, the Cameroon international called the ban, which is effective immediately and applies at national and international level, "excessive and disproportionate."
"I have to say that I respect the UEFA Appeals Body, but I do not share their decision in this case," Onana said.
"I consider it excessive and disproportionate and as it has been acknowledged by UEFA that is was an unintentional mistake."
In the statement, the 24-year-old said he had mistaken the bill containing Furosemide, which had been prescribed to his partner, for aspirin because "the packaging was almost identical."
Furosemide, a diuretic, is used to treat high blood pressure, heart failure and oedema (a buildup of fluid in the body).
It is one of a number of diuretics included on The World Anti-Doping Agency's (WADA) list of prohibited substances.
Diuretics can be used by athletes to excrete water for rapid weight loss and to mask the presence of other banned substances.
"Everyone knows that I lead a very healthy life, and since I started my sporting career, I have always been strongly against any use of doping and I condemn any unsportsmanlike conduct," Onana added.
"I want to say that I have no need to resort to doping to further enhance my sporting career."
Ajax corroborated its player's story, claiming Onana "mistakenly" took the medicine.
"On the morning of October 30, Onana was feeling unwell. He wanted to take a pill to ease the discomfort," the club said in a statement.
"Unknowingly, however, he took Lasimac, a drug that his wife had previously been prescribed. Onana's confusion resulted in him mistakenly taking his wife's medicine, ultimately causing this measure to be taken by UEFA against the goalkeeper."
Onana joined the Dutch club in 2015 and was part of the Ajax side that won the Dutch league in 2019. He has 18 caps for Cameroon.
If the ban is upheld, he will miss the delayed 2021 Africa Cup of Nations. Cameroon is the host nation for the tournament, which has been rearranged for January 2022.
Onana and Ajax have said they will appeal the decision to the Court of Arbitration for Sport (CAS).