Messi's double, as well as goals from Antoine Griezmann, Clement Lenglet and Arthur Melo rounded off an emphatic win at Camp Nou, where Barca successfully bounced back from Saturday's surprise La Liga loss away at Valencia.
"We did a lot of things well but I am not completely happy because we also lost control of the game in the latter stages of the first half," said Setien.
Defeat at Mestalla allowed Real Madrid to pull three points clear at the top of the league and put early pressure on Setien, who replaced Ernesto Valverde as coach earlier this month.
His appointment will be judged on performances in the league and Champions League this season but Barca have a rich recent history in the Copa del Rey, which they have won in four of the last five years.