Although the U's appeared the brighter of the two sides at the off, the Magpies almost took a fourth-minute lead through debutant Enzio Boldewijn.
The Dutchman was able to let rip with a low shot from a good position but visiting goalkeeper Dillon Barnes was able to palm the effort behind for a corner.
But Colchester then threatened midway through the first half through Frank Nouble, whose header from Ryan Jackson's cross flashed inches wide of County's far post.
The hosts received a let off in the second half when keeper Ross Fitzsimons appeared to handle the ball outside of his area after Jackson had sent Nouble through on goal.
Nathan Thomas then came close with a superb chance when he controlled on the edge of the area before trying his luck with a chipped effort, only for Barnes to backtrack and tip the ball over for a corner.
Colchester came close to claiming victory with 15 minutes remaining when Aaron Collins teed up Tom Eastman, who struck the bar with a curled effort from the edge of the box, but ultimately the spoils were shared.
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