"I don't like missing penalties. That's normal. The good thing is that I had the chance to score the other goals," Diego Costa said. "I don't think about my number of goals. I just want to go step by step and hope I can keep scoring. The important thing is that we win, not who scores."
Diego Costa also added that he was ready to play for Spain, a country that had "given him everything" professionally during the past five years.
Celta substitute Manuel "Nolito" Agudo halved the deficit in the 71st and the forward threatened to grab the equalizer late, but a tiring Atletico held on to the three points.
Elsewhere, Valencia drew 1-1 at Athletic Bilbao, Sevilla edged Almeria 2-1 at home, and Getafe beat visitors Real Betis 3-1.
Valencia went in front through Ever Banega's 43rd-minute penalty after Sofiane Feghouli was fouled in the box by Aymeric Laporte, but Bilbao's Mikel Rico equalized in the 76th to leave both teams four points behind fourth-place Villarreal.
Ivan Rakitic headed in Marko Marin's short cross in injury time to give Sevilla the dramatic win over last-place Almeria, which remained the only winless team in the first division.
Getafe eased to its third win in a row thanks to Pedro Leon's two goals and a third from Adrian Colunga. Leon caught Betis goalie Guillermo Sara off his line expecting a cross from his free kick, with the attacking midfielder instead lobbing the ball over the 'keeper and into the net to open the scoring before he headed in a second goal.
Atletico coach Diego Simeone and his players may insist they are not contemplating a challenge for the league title with their mantra of "just going forward game by game," but Celta coach Luis Enrique is one of many who considers them a contender.
"It's not for me to talk about them, but they are the most dangerous opponent we have faced so far," Enrique said. "If they keep playing at this level it would be silly not to consider them for the title."
While Diego Costa continued to impress, his strike partner David Villa had a game he will likely want to forget.
Celta goalkeeper Yoel Rodriguez turned back a number of his shots before Villa wasted a pass from Diego Costa that had left him alone with only the goalkeeper to beat. The 31-year-old Villa aggravated a case of arthritis in his left ankle just before the miss and immediately asked to be substituted in the 58th.
Atletico also lost captain Gabi Fernandez to a left knee sprain late, leading to the debut of French midfielder Joshua Guilavogui.
Rodriguez was particularly outstanding in the 25th when he blocked two clear opportunities following teammate Hugo Mallo's foul of Filipe Luis in the area.
Diego Costa stepped up to take the resulting penalty, but Rodriguez smothered his shot and was quick enough to retreat to his far post to swat away Villa's attempt to poke in the rebound.
But Rodriguez could do nothing when Celta's Alex Lopez knocked the ball back into his own area where Filipe Luis squared for both Diego Godin and Diego Costa to push the ball in. The goal was awarded to Diego Costa.
Diego Costa's second goal came when he neatly chested down a long pass, used one arm to brush off last defender David Costas, and fired the ball under Rodriguez.
"Costa is our soul," said Simeone. "He played a great game. He is constantly growing and can get even better."
Both Atletico and Barcelona can match Madrid's record start of nine consecutive wins to start the season in 1968 in the next round after the international break.
