Atletico's 11th win in 12 rounds left it one point behind leader Barcelona, which has 34 points following its 1-0 win over Espanyol on Friday. Real Madrid, which beat Rayo Vallecano 3-2 on Saturday, is third in the standings with 28 points.
"We're not frustrated that Barcelona keeps winning. We're just happy to keep competing with them after so many rounds," Simeone said.
Also on Sunday, Valencia lifted some of the pressure of coach Miroslav Djukic with its first win in five rounds, a 1-0 victory at Getafe. Granada scored in stoppage time for a 1-0 win at Levante, while Malaga also needed an injury time winner from a late substitute to beat Real Betis 3-2.
Costa, the Brazilian-born, naturalized Spaniard, has spearheaded Atletico's title credentials so far this season. But it was captain Gabi who first tested Iraizoz in the 18th, and the Basque goalie made an outstanding reaction save to a low drive.
Costa then showed how dangerous he is when given space in front of goal as he moved freely down the left side to poke a shot past Iraizoz, but also beyond the far post.
Atletico controlled a physical game and was inching closer to an opener as Iraizoz made another reaction save to deny Villa's powerful half-volley in the 26th.
But Iraizoz couldn't keep up with the Spanish striker's shot from almost the same spot moments later, as Villa's sixth goal of the season made it 1-0.
Koke has been instrumental in Costa's scoring run and the Spain midfielder again set up the striker to add the second, putting him even with Cristiano Ronaldo atop the scoring chart.
"He's such a great player who is growing in every area," Simeone said of Costa, who had chances to score several more over the closing stages. "He's getting better in every aspect, from recovering the ball, controlling it, his movement, and that is helping the team play better."
Valencia had lost three straight before the game at the Alfonso Perez Stadium but an impressive first-half strike from Dorlan Pabon sealed the morale-boosting victory.
The Colombian striker unleashed a powerful shot from 30 meters in the 40th minute that flew beyond goalkeeper Miguel Angel Moya into the left corner.
Athletic is fifth with 20 points, one more than Getafe. Levante is on 17 points, while crosstown club Valencia has 16.
Levante had a penalty in the 25th, but midfielder Nabil El Zhar saw his spot kick saved by Roberto Fernandez.
That left the game scoreless until Keylor Navas was beaten by Piti's free kick, although Granada teammate Manuel Iturra likely distracted the Levante goalkeeper as he stood alone between him and the defensive wall as the ball spun over and in.
Meanwhile, Roque Santa Cruz and Eliseu put Malaga ahead in each half only for Joan Verdu to cancel out the opener with a 33rd-minute free kick, and Jordi Figueras to equalize again with an angled header in the 61st.
But Malaga substitute Samuel Sanchez scored in the fourth minute of added time by volleying in a rebound after Francisco Portillo's effort came off the crossbar.
Six minutes of added time were added after Betis defender Damien Perquis was taken from the field in an ambulance after colliding with Fabrice Olinga in the 55th.
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