Antoine Griezmann's controversial penalty looked to have given Atletico a 1-0 win to cut Barcelona's lead at the top of the table to eight points.
But after Greizmann was substituted, having missed a great chance to seal the points, Unal stuck twice in the last 10 minutes to snatch victory for the hosts.
But bringing on Vitolo for Angel Correa backfired — the winger was sent off in injury-time after a clash with Nicola Sansone — while the decision to gamble by introducing striker Fernando Torres for Koke with the score at 1-1 left Atleti overrun.
Unal slipped in unmarked at the back post to extend Atleti's winless run against Villarreal to six matches and Simeone took the blame.
"I have the feeling that I lost the game myself," Simeone said.
"The players made a huge effort and I could not help them with my decisions. I may have been wrong.
"It was an intense match with similar characteristics in both teams, we made a good first half and we were handling it well in the second and they took advantage of those two actions.
"The details caused the match to fall on their side in such a close game."
THAT FEELING ! pic.twitter.com/7kp88sQNyO— Villarreal CF (@VillarrealCF) March 18, 2018
Atletico were on track to win their 12th game in 13 matches in all competitions before their late collapse, a narrow defeat at Barcelona the only result blotting their recent form.
But even though a 2-1 loss at Villarreal leaves his side 11 points behind Barca with only nine games to play, Simeone is not yet ready to give up hope.
"We are still on the same line, trying to do as much as possible," Simeone said.
"We did many good things, others bad, but we still think about adding many points.
"We have to add many points and we will see in the last five days where we are."
While Simeone held his hands up regarding tactical decisions, Saul Niguez blamed Atletico's defending of set-pieces for their loss.
"We have no explanation, they have taken advantage of the fact that they have not defended well those two set plays, today we started well but two tactical errors cost us the game," Saul told beIN Sports.
"Their set pieces are different, they are strong in that aspect and they have beaten us with them.
"We should not think about the league, but focus on our matches and do things right."