No matter what happens in the final four games of the season, the Rojiblancos will at least finish the season in fourth spot in La Liga, entitling them to a play-off place in Europe's elite competition.
If they win two of their remaining games, they will be guaranteed third spot and earn an automatic berth in the tournament.
The point means Deportivo stay one point ahead of the relegation zone, but they could find themselves back among the bottom three if Real Zaragoza beat Rayo Vallecano on Sunday.
The Galicians did not show much ambition to win the game, but had three penalty appeals turned down, replays showing they should have at least been awarded one.
The game was played at an energetic pace but was short on quality football.
Deportivo's chances were limited to long-range efforts, none of which troubled visiting keeper Thibaut Courtois too much, while Atletico's tactics consisted of putting in failed crosses towards Falcao, who was isolated up front on his own due to the absence of the team's other focal point in attack, Diego Costa, who was suspended.
The best chance of the first half fell to Atletico.
Raul Garcia put in a cross from the right-hand side to Miranda at the far post. The Brazilian failed to connect properly with the ball and it fell to Diego Godin 10 yards out, but the centre-back took too long to get his shot away and Deportivo defender Ze Castro made the block.
The home side were aggrieved not to be awarded a penalty on 33 minutes when Bruno Gama entered the box and appeared to be tripped by Miranda, but referee Miguel Angel Ayza Gamez waved play on.
The second half saw an even smaller number of chances.
Deportivo appealed for another penalty when the ball struck Atletico left-back Filipe Luis' shoulder in the box, but their claims had less conviction than the incident in the first half.
With 10 minutes remaining, Gabi produced the most exciting moment of the match from out of nowhere. The Atletico midfielder tried his luck on goal from 30 yards out and his shot struck the crossbar, the closest either team came to scoring all game.
Atletico thought they had finally scored in the 89th minute when Miranda appeared to flick a cross from a set-piece into the bottom corner, but the goal was ruled offside.
Diego Simeone's side continued to press for a winner but Deportivo launched a counter-attack in stoppage time.
Substitute Evaldo received the ball in the area and went for goal. His effort appeared to be blocked by the hands of Atletico full-back Juanfran, but Ayza Gamez only gave a corner, to the fury of the Deportivo players.