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."
Colchester 44 Walker 04 Okuonghae 18 Eastman 20 Wilson 23 Olufemi 02 Wright (Gilbey - 64' ) 06 Eastmond 07 Watt (Wright - 85' ) 11 Sears 21 Massey 17 Ibehre Substitutes 01 Cousins 05 Thompson 14 Bond 15 Bean 22 Gilbey 09 Morrison 30 Wright Carlisle United 01 Gillespie 05 Livesey 06 Black 12 Thirlwell Booked 28 Butterfield 03 Robson (Gillies - 86' ) 07 Amoo (Symington - 90' ) 08 Noble Booked (Guy - 76' ) 16 Potts Booked 21 Berrett Booked 09 Miller Substitutes 20 Fleming 02 Feely 14 Gillies 19 Symington 10 Campbell 17 Beck 29 Guy