Marc Pubill's stunning strike from distance put Atletico Madrid ahead in the 59th minute before Villarreal responded with two penalties either side of Robin Le Normand's 76th-minute red card, with Gerard Moreno and Georges Mikautadze on target from the spot before Atlético salvaged a point in a chaotic finish.
Álvarez, introduced as a substitute, left the pitch alone at the end without approaching the home supporters.
Simeone explained that decision was made by the club rather than the player himself.
"People at the club told me that the club decided he shouldn't go over to the stand and his people. The decision was the club's, to keep him away and separate him, so he'd come straight to the dressing room."
Asked whether he had any advice for Álvarez amid the ongoing transfer saga, Simeone kept his focus on football matters.
"I'm not here to give advice. I have to focus on my job, which is to give my best from a sporting point of view. If we want to win a title we need to stick together, have forwards and have important forwards."
He declined to be drawn further: "I'm not going to answer every question about Julián. I understand the concern and we can talk about what happened in the match."
On the performance itself, Simeone felt his side controlled proceedings for long periods.
"The team controlled the game, showed an important defensive face, working quite well despite Oblak's saves being needed. Against a team with important attacking players, the best counter-attackers in LaLiga, we took charge of the game we had to play. We went ahead with a great goal from Pubill and we lacked management of the time that followed. I'm not going to dwell on the penalties, whether they were right or not, they've already been given. We had to make an incredible effort."
Simeone also offered an unusual apology to Ademola Lookman for asking him to play as a central striker in Álvarez's continued absence from full fitness.
"Apologising to Lookman, I know it's not his position. He had to help us, because Sørloth is injured and Julián is getting into his best shape. He's a noble lad who works hard, but he lacked what he enjoys, which is dribbling, having goals, one-against-one situations, and we'll give that back to him when we have our forwards available."
Villarreal's new head coach Íñigo Pérez, taking charge for the first time in LaLiga away at the Metropolitano, felt his side had shown genuine improvement despite conceding two goals.
"When it seems like it's easier, or your subconscious sends you messages that the situation is under control, that's when you relax. The energy, the enthusiasm of this coach, this team and this support made it count, and that's what happened. I don't think we interpreted it correctly at that point, but beyond that, I agree the rest of the match was interpreted perfectly."
Pérez pointed to Villarreal's mentality in fighting back after going behind.
"Playing a match you've imagined, that you've practised in training, that's going well, then conceding a goal and staying with that same idea and getting two goals speaks to a good mentality in this team. Every coach tries to instil that, but the players have it inside them."
On the four goals conceded so far this season, he added: "Two are shots from outside the box, and the other is a penalty we concede in an absurd way. I don't think it worries me at all to have conceded four goals, I think it's part of this process."