Matt Fryatt was just a whisker away from getting his head onto the end of a Levi Porter free-kick when Leicester carved out their first real opportunity after 10 minutes.
Then Colchester were lucky to survive claims for a penalty when Wayne Brown barged over Chris O'Grady inside the box.
United's only clear chance in the first half arrived on 17 minutes when a mistake by Patrick McCarthy let in Jamie Cureton who screwed his shot wide.
On the half-hour mark O'Grady fired just wide after the visitors failed to clear Gareth McAuley's free-kick.
Moments later James Wesolowski tried his luck from distance with the keeper needing two attempts to kill the ball with Fryatt ready to pounce.
The Foxes should have gone in front a minute before the break when Porter crossed to the far post, but Fryatt and O'Grady got in each other's way and the chance was gone.
Within moments of the restart it was Colchester that squandered a clear chance when Cureton played in Karl Duguid who side-footed wide from 10 yards with the goal at his mercy.
Iain Hume almost crowned his arrival as a 68th minute substitute but he was unable to get a clean connection on a Josh Low cross.
Chris Barker was lucky to escape with just a yellow card on 72 minutes when he hacked down Fryatt as City sought to break quickly.
Then, with nine minutes remaining, Hume appeared odds-on to break the deadlock when he raced on to Porter's pass over the top of the Colchester defence but Aidan Davison had spotted the danger and sprinted from his goal to hack the ball clear.