Goals from Antoine Griezmann, Angel Correa and Kevin Gameiro ensured Atletico will go into next Wednesday's second leg with a commanding lead after a routine victory at the Vicente Calderon.
Eibar's slack defending made it a comfortable win for Atletico, with Simeone highlighting the positive impact of Yannick Carrasco and the improving Nicolas Gaitan, along with the trio of scorers.
"It was an important game, we backed the team to win duels one against one," Simeone said.
"With the speed of Griezmann, Correa, Carrasco and Gaitan, which is fine, we could do damage. With some precision we were going to have chances and the match was good.
[Gaitan] has been working well, he has had a major change since November in terms of his adaptation and what the team needs from him, if you add talent to work you approach the ideal situation," he said of the Argentine, who joined Atleti from Benfica in June.
Correa's goal was the 500th Atletico have scored since Simeone took charge in 2011 and the Argentine said he is pleased with the club's recent progress after recording their fourth home win in five games from all competitions.
"I'm happy with the victory, the team's response to a major game, and how they have been competing for five years," Simeone said.
"Today we only care what is done today and what we have to do on Sunday [against Athletic Bilbao in LaLiga].
"We look with the same… desire to compete and that will remain as long as I am in charge of the team."
Jose Maria Gimenez was given a chance to impress in the Atletico defence and the Uruguayan centre-back insisted the tie is not over despite his team's three-goal lead after the first leg.
"In the first half Eibar defended well, but in the second half we managed to get two more goals that give us [some comfort], but that does not close the tie at all," he told Bein Sports.
"We are not going to relax a little bit, we know the difficulties of all the LaLiga teams… the advantage is quite favourable for us, but it [the outcome of the tie] is not closed."