Critically Endangered Animals Conservation Act of 2021 This bill provides statutory authority for the Critically Endangered Animals Conservation Fund, which finances a grant program to protect critically endangered species. Specifically, the bill requires the Department of the Interior to establish the fund as a separate account in the Multinational Species Conservation Fund. Critically endangered species means any animal species categorized on the International Union for Conservation of Nature (IUCN) Red List of Threatened Species as either endangered or critically endangered. The term also means any other animals species categorized on such list as data deficient or under a threat category lower than endangered if Interior determines that (1) the most recent IUCN Red List assessment indicates that the population is decreasing, or (2) such species is facing new or emerging threats.