Crawley have now gone eight games without a win but fashioned the best chance of the night when Malone's cross found Dion Pereira and his downward header was kept out by the knees of Matt Macey in the Colchester goal.
Late in the game, Ronan Darcy also forced a save out of Macey at his near post as he shot on the turn but otherwise it was a second half of holding out for a point by the visitors.
The most serious pressure from the hosts came in the final quarter as Danny Cowley threw on three substitutes and they forced a series of corners.
Jaden Williams shot over with his left boot from 10 yards out before Will Goodwin saw his close-range effort well blocked.
Goodwin was then sent clear into the area but decided to try and square for Williams and a poor pass allowed the clearance to be made.
The next week could make or break Colchester's season as they visit second-placed MK Dons on Wednesday, before a trip to leaders Bromley next Saturday.
Crawley face play-off chasing Barnet and Fleetwood in their upcoming fixtures.