Gavin Massey gave the visitors the lead just before half-time and Michael Smith extended their lead midway through the second half.
Substitute Callum Wilson quickly got the Sky Blues back into the game before captain Carl Baker levelled things up in injury time.
Coventry had three good chances in the first nine minutes - the pick of the bunch falling to Cody McDonald but the striker fired against the post after holding off a two defenders.
Colchester grew in confidence as the first half went on and they took the lead in the 39th minute through Massey, who latched onto a loose ball in the box and struck home from 12 yards.
The home side were on top at the start of the second half but, just the like the first half, were left to rue missed chances.
In the 72nd minute, struggling Colchester thought they had sealed the win when Clinton Morrison flicked on a looping ball and Smith calmly finished underneath goalkeeper Joe Murphy.
Sub Wilson reduced the deficit in the 77th minute with a great run and finish and then Baker fired home a free-kick in injury time to earn a point for his new manager.