Dropped points no huge concern, says Simeone
The Spaniard was full of praise for his players, who held the lead before conceding a late goal to Ikechukwu Uche.
Simeone admitted his team had struggled offensively during the game as Villarreal controlled possession.
"We never attacked how we wanted, maybe a bit more in the second half, especially with that header from David Villa," Simeone said.
"So this was a good point for us against a rival who will be fighting for the same things as us this season.
"I want to congratulate my players for this, for their huge effort."
The Atletico boss felt his team did well to deny Villarreal too many chances at goal.
"We faced a team that plays good football, they are in good form at the moment, so defensively we had to make a big effort," he said.
"They didn't get many chances but they did have the control of the ball."
Simeone had a lot of respect for the way Villarreal played out the match.
"It was hard for us to attack, to find good combinations and spaces," Simeone said.
"They forced us to defend in our own box.
"We couldn't make good transitions from defending to attacking as we normally do," he said.