Braces from Rodrigo Moreno and Paco Alcacer ensured Spain retained their 100 per cent record in Euro 2020 qualifying Group F, and helped new coach Moreno to a second win in two games since he took over on a permanent basis.
The players of both sides observed a minute's silence before Sunday's game as a mark of respect to Luis Enrique, who was born in Gijon where the match was played.
"It upsets me to talk about it, but this team is his [Luis Enrique's] more than anyone's," Moreno told a news conference.
"It is a tiny thing, but we wanted to dedicate it, especially here in El Molinon."
After seeing his players labour at times against a Faroe Islands team that put 10 men behind the ball for much of the game, Moreno praised Spain's goal-scorers.
"I leave very satisfied," he said.
"It is a privilege to have a scorer like Alcacer, who is very good in the area. But Rodrigo has also scored two others, and I am happy because the two have succeeded.
"Alcacer increases competition, and you have to score a goal every game [to compete with him]."
Moreno also paid tribute to Sergio Ramos, who equalled Iker Casillas' record of 167 appearances for Spain on the night and said the win, which came after nine changes to the line-up that started in Spain's 2-1 victory over Romania on Thursday, increased competition for places.
"There are several ways to get into the national team," Moreno said.
"First, do well with your clubs, and then do well and do your best when playing for Spain.
"It has been a good week, because it increases internal competition. And that is very good for the national team, although it is more difficult for me to choose."
Spain are top of Group F for Euro 2020 qualifying having won all six of their games to date.