Atletico pushed hard throughout the second half for a winner, with Joao Felix, Koke and Luis Suarez threatening, and home goalkeeper Guilherme playing a blinder.
But the goal they were searching for proved elusive, when with a little more luck and a touch more precision they might have won by two or three.
The Spanish visitors had gone ahead early on thanks to a terrific header from Jose Gimenez before being frustrated to give away the penalty from which Anton Miranchuk tucked in the home side's equaliser midway through the first half.
Gimenez made the breakthrough for coach Simeone's team in the 18th minute. Hector Herrera's cross from the left picked out the run into the penalty box by the Uruguayan, who leapt well before directing a header into the bottom-left corner.
Lokomotiv were awarded their penalty in the 22nd minute when a ball into the box brushed Herrera's right arm. Referee Benoit Bastien went to a VAR review before making a decision that angered Luis Suarez so greatly he was booked for his protests.
Miranchuk slotted into the left corner after a stuttering run-up, as Jan Oblak dived the other way.
Angel Correa struck the Lokomotiv crossbar with a 20-yard shot, before Suarez sent a volley too high, as Atletico looked to regain the lead.
Atletico came into this game, which was watched by around 8,000 spectators, after beginning their Group A campaign with a 4-0 defeat at Bayern Munich and a 3-2 victory over Salzburg.
Suarez threatened with a header from a tight angle early in the second half, before Joao Felix was denied a wondergoal by a fingertip save from Guilherme, his whipped 25-yard strike having been arrowing towards the top-right corner.
Joao Felix was denied again by the goalkeeper, touching over his powerful header, before Koke hit the bar, also with a thumping header. Suarez tapped in as the ball rebounded out but had strayed offside. It was not to be their night.
What does it mean? Lokomotiv running out of time
For Lokomotiv, after drawing with Salzburg and losing 2-1 to Bayern, this felt like a must-win game ahead of tricky trips to Madrid and Munich later in the campaign. They were backed by noisy home supporters, which meant there was a real vibrancy to the game, but had to cling on at the end. Atletico and Bayern have always looked the class acts in this group, and nothing in this game changes that perception.
Joao Felix was eminently watchable as he looked to cause devastation in the final third, but Herrera was terrific throughout, and mighty unfortunate to give away the penalty when his hands were slightly raised. Herrera attempted 91 passes - 21 more than anyone else in Atletico blue - and his cross for the opener showed great vision.
Atletico played through Herrera, as his team-high 103 touches showed, and his fine showing came on the night he made his 46th Champions League appearance - equalling Javier Hernandez's record for the most games played by a Mexican in the competition.
46 - @atletienglish's Héctor Herrera will make his 46th appearance in the @ChampionsLeague, equalling Chicharito Hernández as the Mexican with the most apps in the competition. Elite. pic.twitter.com/Mv6c7IhYFD— OptaJorge (@OptaJorge) November 3, 2020
Atletico out of luck
There was a lot to like about Atletico's performance, but strikers must put away chances to win games in the Champions League. Joao Felix had five goal attempts and Suarez three, and they are certainly approaching a good understanding, with the latter hoping his new team-mate can be as helpful as Lionel Messi often was at Barcelona.
Joao Felix fed the ball to Atletico's number nine four times, and next time he might convert one of those passes.
Key Opta Facts
-Atletico have failed to keep a clean sheet in any of their previous five matches in the Champions League, their worst run in the competition since a seven-game stretch ending in October 2013.
-Los Colchoneros have also won just one of their past five away games in the competition (D1 L3), with that win coming against Liverpool at Anfield in March.
-With this draw, Atletico have a solitary triumph from their opening three Champions League group games this season – the only two previous seasons in which they have won as few at this stage are 2009-10 and 2017-18 (zero victories), being eliminated on both occasions.
-Lokomotiv scored with their only shot on target in this match, courtesy of Miranchuk's 25th minute penalty.
Atletico face Cadiz in LaLiga on Saturday, in their last match before the international break. Lokomotiv have a derby clash with Dinamo Moscow ahead of them on Sunday.