Victory at Atletico's Calderon stadium would have put Unai Emery's side seven points clear of Levante after their city rivals drew 1-1 at home to Racing Santander on Saturday.
They managed to check Atletico's resurgence under new coach Diego Simeone but ultimately appeared happy to settle for a point - and their third draw in a row - with Wednesday's King's Cup semi-final second leg at Barcelona looming.
Atletico had drawn one and won three on the trot in the league since Simeone's appointment at the end of last year and looked the more threatening of the two sides on a chilly night in the Spanish capital.
In a game littered with fouls, striker Radamel Falcao had the home side's best chance midway through the second half but his close-range effort was cleared off the line by Valencia defender Adil Rami.
Leaders Real and second-placed Barca both won on Saturday, preserving Real's seven-point advantage over the champions with just under half the season left.
Real's 1-0 success at Madrid neighbours Getafe lifted them to 55 points from 21 matches, with Barca on 48 following a 2-1 win at home to Real Sociedad.
Valencia are now 11 points behind Barca on 37, underlining the dominance of the world's two wealthiest clubs by income. Levante have 32 points, level with fifth-placed Espanyol but ahead on goal difference, and Atletico are seventh on 30 points.
HEADS BOWED
Sevilla slipped deeper into crisis when they were beaten 2-1 at home by improving Villarreal earlier on Sunday, a seventh straight game without a win which left the Andalusians only four points above the relegation places.
Borja Valero volleyed the visitors in front in the 20th minute at the Sanchez Pizjuan before a Jesus Navas centre was turned into his own net by Villarreal midfielder Bruno Soriano in the 33rd to make it 1-1.
Javier Camunas clipped home the winner nine minutes from time and the stadium erupted in booing and whistling at the end of the game as the home players and coach Marcelino trooped off down the tunnel with heads bowed.
"The results are negative but I will continue working until those who make the decisions decide otherwise," Marcelino, who was appointed in June, told a news conference.
"I will not throw in the towel and I know where I am coming from and with what high hopes I arrived here."
In a congested lower half of the table, where six points separate eighth from 18th, Sevilla are 11th on 26 points from 21 matches, while Villarreal's revival after an injury-hit season continued as they climbed out of the relegation places to 16th on 23 points.
Struggling Sporting Gijon, who sacked long-serving coach Manuel Preciado on Tuesday and are yet to appoint a replacement, conceded a goal 13 minutes from time to draw 1-1 at home to mid-table Osasuna in the earlier kick-off and are 19th.
