The Pilgrims are already assured of promotion but were hoping to turn up the heat on League Two leaders Doncaster with a win.
Colchester also have promotion in their sights but lost ground in the play-off race after dropping points in their penultimate home game.
Despite the lack of goals, both sides had chances during an absorbing contest.
Colchester's best effort was a miscued, close-range header from Chris Porter, after a teasing left-wing delivery from Brennan Dickenson.
Porter then screwed another low effort agonisingly wide, this time from Drey Wright's cross.
Plymouth's Antoni Sarcevic got clear down the right after being played in by Graham Carey but his powerful shot flashed wide of the right post.
The Pilgrims went close after a corner from the left appeared to be deflected goalwards by U's defender George Elokobi, before being safely gathered by Sam Walker.
Match report supplied by the Press Association.
Match ends, Colchester United 0, Plymouth Argyle 0.
Second Half ends, Colchester United 0, Plymouth Argyle 0.
Attempt missed. Jordan Slew (Plymouth Argyle) right footed shot from outside the box is close, but misses to the left.
Attempt missed. Brennan Dickenson (Colchester United) left footed shot from outside the box is just a bit too high.
Chris Porter (Colchester United) wins a free kick on the right wing.
Foul by Gary Sawyer (Plymouth Argyle).
Attempt missed. Chris Porter (Colchester United) header from the centre of the box is too high following a set piece situation.
Antoni Sarcevic (Plymouth Argyle) is shown the yellow card for a bad foul.
Brennan Dickenson (Colchester United) wins a free kick in the attacking half.
Foul by Antoni Sarcevic (Plymouth Argyle).
Foul by Brennan Dickenson (Colchester United).
Oscar Threlkeld (Plymouth Argyle) wins a free kick in the defensive half.
Substitution, Plymouth Argyle. Craig Tanner replaces David Fox.
Attempt saved. Paul Garita (Plymouth Argyle) header from the centre of the box is saved in the top centre of the goal.
Corner,  Plymouth Argyle. Conceded by Tom Eastman.
Corner,  Plymouth Argyle. Conceded by George Elokobi.
Attempt saved. Doug Loft (Colchester United) left footed shot from outside the box is saved in the centre of the goal.
Attempt missed. Chris Porter (Colchester United) left footed shot from the centre of the box is close, but misses to the left.
Attempt missed. Graham Carey (Plymouth Argyle) left footed shot from outside the box is close, but misses to the right.
Richard Brindley (Colchester United) is shown the yellow card for a bad foul.
Foul by Richard Brindley (Colchester United).
Graham Carey (Plymouth Argyle) wins a free kick on the right wing.
Substitution, Colchester United. Doug Loft replaces Tom Lapslie.
Attempt missed. Oscar Threlkeld (Plymouth Argyle) right footed shot from the right side of the box misses to the right.
Hand ball by Paul Garita (Plymouth Argyle).
Substitution, Colchester United. Rekeil Pyke replaces Tarique Fosu-Henry.
Hand ball by Jakub Sokolik (Plymouth Argyle).
Corner,  Plymouth Argyle. Conceded by George Elokobi.
Chris Porter (Colchester United) wins a free kick in the attacking half.
Foul by Yann Songo'o (Plymouth Argyle).
Substitution, Plymouth Argyle. Jordan Slew replaces Jake Jervis.
Attempt missed. Graham Carey (Plymouth Argyle) left footed shot from the right side of the box misses to the left.
Corner,  Colchester United. Conceded by David Fox.
Attempt saved. Chris Porter (Colchester United) header from the centre of the box is saved in the centre of the goal.
Corner,  Colchester United. Conceded by Gary Sawyer.
Attempt blocked. Drey Wright (Colchester United) right footed shot from outside the box is blocked.
Attempt missed. Brennan Dickenson (Colchester United) header from the centre of the box misses to the left following a corner.
Corner,  Colchester United. Conceded by Oscar Threlkeld.
Chris Porter (Colchester United) wins a free kick in the defensive half.
Foul by Yann Songo'o (Plymouth Argyle).
League Two title-chasing Plymouth were forced to share the spoils with Colchester United after they played out a goalless draw at the Weston Homes Community Stadium.