Liverpool completely dominated this Champions League Group A game but lacked a final cutting edge.
After John Arne Riise had cleared Cesar Martin's header off the line, Liverpool created a stream of good chances.
But Manuel Pablo made a couple of superb tackles to steal the ball from Djibril Cisse and Milan Baros.
And goalkeeper Jose Molina also made three vital stops, foiling Cisse twice and also denying Luis Garcia when the Liverpool striker was in the clear.
The draw means Liverpool are likely to have to pick up points from a couple of tricky away games against Deportivo and Monaco if Rafael Benitez's side are to progress to the knockout stages.
If the result was disappointing given Liverpool's dominance, the performance provided some encouraging signs of Benitez's evolving side.
Xabi Alonso was superb in midfield, while Milan Baros also worked tirelessly for little reward.
The much derided Djimi Traore also played impressively at left-back.
After Riise had to rescue Liverpool on 15 minutes when he cleared Martin's header off the line after a Deportivo corner, the visitors barely threatened the Liverpool goal as Alonso took control in midfield.
The Deportivo full-back Pablo had to be just as conscientious as Riise in his defensive duties when he rushed across to block a Cisse effort, the first of those succession of Liverpool chances.
After more good work by the industrious Baros down the right, Cisse did manage to get his shot away when his half-volley drew a reaction save from Molina.
And Pablo had to make another superb defensive intervention when he raced back to steal the ball off Baros' toes after the Czech Republic striker rounded Molina.
It was then the turn of Molina to rescue his side when he tipped over the bar Luis Garcia's rising shot after Alonso's vicious effort richocheted into the former Barcelona striker's path.
Alonso's quick thinking and vision allowed him to create yet another Liverpool chance just before the interval when he picked out Baros
from a free-kick.
The Liverpool striker span away from a posse of Deportivo defenders and arrowed a shot narrowly wide.
On the hour Chris Kirkland's indecision almost allowed Juan Carlos Valeron to pick up Victor Sanchez's cross, but the Deportivo forward was unable to get the ball under control quickly enough.
Rafael Benitez introduced Harry Kewell and the Australian immediately produced a cross that found Cisse, who again tested Molina with a low shot.
And Kewell almost snatched the win in stoppage time when his free-kick whistled past the post.
Liverpool: Kirkland, Josemi, Hyypia, Carragher, Traore,
Luis Garcia (Sinama Pongolle 84), Alonso, Hamann,
Riise (Kewell 66), Baros, Cisse (Finnan 76).
Subs Not Used: Dudek, Diao, Biscan, Warnock.
Booked: Hamann, Baros.
D Coruna: Molina, Manuel Pablo, Cesar, Andrade, Capdevila,
Victor, Mauro Silva (Scaloni 58), Duscher, Luque,
Valeron (Fran 86), Pandiani (Romero 82).
Subs Not Used: Munua, Tristan, Munitis, Pablo Amo.
Booked: Luque, Andrade, Duscher, Victor.
Ref: Anders Frisk (Sweden).