Atletico struggled to create many chances of note against an organised Espanyol defence and needed a single Antoine Griezmann strike late in the second half to emerge victorious.
Simeone was delighted with his side's win just days after they booked their ticket to the Champions League semi-finals at the expense of Leicester City, but he did acknowledge Espanyol put up a strong fight.
"It was an even match and the decisiveness we showed in front of goal is the reason we took the three points," the Atleti boss said at a news conference.
"After reaching the semi-finals of the Champions League, this was important. We have some tough opponents coming up in LaLiga and next up we play Villarreal, who should be fighting for third too given the players they have. After that we must go to Las Palmas, so there is a lot up ahead.
"Espanyol played a good game. As a team, they work really well and they lead you into situations where you lose the ball, where space is created and where they can hurt you on the counter-attack. The first half was quite disorganised, but the second half was more balanced."