Prime Minister Leo Varadkar had pitched the vote, held on Friday to coincide with International Women's Day and counted on Saturday, as a chance to delete some "very old-fashioned, very sexist language about women".
A proposal to expand the definition of family from a relationship founded on marriage to include other durable relationships was rejected by 67.7% to 32.3%.
A second referendum on a proposal to replace language surrounding a woman's duties in the home with a clause recognising the role of family members in the provision of care was rejected by 73.9% to 26.1%.
Campaigners argued the proposal would enshrine care as a private responsibility, and not a state one.
Speaking to reporters in Dublin on Saturday, Varadkar said voters had given his government "two wallops".
"It was our responsibility to convince a majority of people to vote yes, and we clearly failed to do so."
