Carlisle grabbed a first point of the season but Freddie Sears hit a 71st-minute goal to deny them victory.
Matty Robson fired Carlisle ahead from 20 yards before U's duo Brian Wilson and Jabo Ibehre had shots saved by visiting goalkeeper Mark Gillespie.
The visitors had a goal disallowed as Liam Noble was ruled offside and soon after Sears lashed home a neat chest down from strike partner Gavin Massey.
Ibehre then thought he had won it only to see a late shot flash inches wide.
VIEW FROM THE DRESSING ROOM
Colchester United manager Joe Dunne told BBC Essex:
"We felt if we moved the ball, we'd get opportunities, and we had opportunities galore.
"I can't fault the players one bit. I thought we were outstanding.
"Great credit to them (Carlisle), they hung on in there. I think if we'd got that second goal, we would have scored more.
"We've played some really exhilarating football, there was good quality on show."
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