If a match ended level at full time, a replay was required to decide the winner.
William Morrow of Moyola Park scored the first goal in an Irish Cup final during his club's 1–0 win over Cliftonville to lift the trophy.
The draw for the first round was made on 10 January 1881, with the matches played on Saturday, 5 February 1881.
Alexander received a bye into the semi-finals as a result of the odd number of seven participants.
[1] The inaugural Irish Cup final was played on 9 April 1881 at the Cliftonville Cricket Ground, Belfast in front of 1,500 spectators.