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.