Rory Fallon put United ahead with a header, after the Iron dominated the opening stages, and former Iron forward Freddie Sears drew the U’s level shortly after half an hour.
The second half was a scrappy exchange as neither side could find a second.
It was Robins’ first match in charge after signing a three-year deal to become United’s manager on Monday.
The Iron began the match with an unchanged eleven from the team which won at Gillingham last week.
Sam Slocombe returned to the matchday squad for the first time since injuring his shoulder against Blackburn in August, with the club captain settling for a place on the bench.
There was a debut appearance for Isaiah Osbourne, who joined the club on a short-term deal on Friday. He came off the bench after half-time, replacing Sean McAllister.
Colchester arrived in North Lincolnshire in 17th place and on the back of a 2-1 victory over Fleetwood last weekend and Tony Humes’ side were full of confidence, having won two of their last three.
The home side had the better start though, pinning back Colchester in their own half as Paddy Madden and Jennison Myrie-Williams went close with early efforts, with the latter pulling a low shot just past the post.
David Fox went closest in the opening 15 minutes with a stunning effort. The visitors’ free-kick into the box was headed clear and he hit a thunderous half-volley, which was set to nestle in the roof of the net, and Bobby Olejnik did terrifically well to save and keep hold of the ball.
Freddie Sears failed to find an opening as Olejnik stopped his tame shot comfortably, but Scunthorpe continued to press. Good play saw Luke O’Neill find space to cross and it just missed the head of Fallon.
Former Iron loanee Sears went close as Colchester counter-attacked and Gavin Massey crossed before the former West Ham man struck the ball with his knee and rattled the crossbar.
The game’s tempo began to increase as the Iron quickly attacked and Madden shot over from 22 yards.
The opening goal came on 20 minutes for the Iron. Quick feet by Myrie-Williams earned the home side a free-kick on the left-hand corner of the box. McSheffrey crossed the resulting set-piece to the edge of the six-yard box, where Fallon headed home for his third goal in five appearances for the club this season.
They could have doubled their lead within five minutes as Madden found space in the box and he was through one-on-one, his placed shot went just over the crossbar.
Sears drew the Essex side level on 33 minutes, after a period of ball retention from the visitors. He was found by David Fox on the edge of the box and he turned to clinically strike his seventh goal of the season into the far corner. Sears, who played nine times for Scunthorpe in a two-month loan spell in 2010, did not celebrate against his former club out of respect.
The goal put the U’s on top for period before the break and George Moncur tried his luck from around 25 yards and Andrew Boyce blocked his goal-bound effort.
Sears soon fired a 20-yard free-kick over as the U’s finished the first half on top but McSheffrey had an effort saved after Madden passed inside to him and he let the ball run across his body before striking low to the near-post and Sam Walker got behind it well.
The visitors continued to push for a second goal after the restart, with Sanchez Watt going closest as he pulled his shot wide from the right.
Gary McSheffrey was set through and Walker was quick out of his goal to collect and the former Coventry man was booked after colliding with the visiting goalkeeper.
A quick Colchester attack down the left by Watt, who showed a superb burst of pace, saw the ball pulled inside and Alex Gilbey failed to hit the target from 18 yards.
Substitute Lyle Taylor looked dangerous as he nearly put through Madden, as his pass was well read by defender Tom Eastman.
Marcus Williams looked to have put Taylor through with a long ball into the box, but the former Sheffield United man failed to control the high ball.
McSheffrey’s corner was cleared and O’Neill hit a low cross into the box to Madden, who controlled and shot but ‘keeper Walker was well positioned to save the Irishman’s effort.
Sears and Gilbey linked up well for Colchester at the other end and Boyce’s last-ditch interception proved crucial as the latter would have been through on goal.
Three sides of Glanford Park were appealing for a penalty as Eastman’s backwards header put Madden through on goal and the forward’s shirt was clearly pulled back and referee David Coote waved away the claims.
Colchester nearly got a second instantly after the penalty claim, when a goal-mouth scramble saw Massey miss a couple of efforts before Moncur fired over from ten yards.
The visitors piled on the pressure late on with a series of corners but the Iron held firm, even in added time of the match, as Olejnik came to the rescue as he tipped Healey’s effort against the post to earn the Iron a point.
Scunthorpe United: Olejnik, O'Neill, Boyce, Brisley, Williams, Myrie-Williams, Bishop (c), McAllister (Osbourne, 45), McSheffrey (Adelakun, 75), Madden, Fallon (Taylor, 45).
Substitutes not used: Slocombe, Burton, Kee, Llera.
Colchester United: Walker, Watt (Healey, 72), Gilbey, Sears, Eastman, Clohessy (c), Massey, Moncur, Kent, Fox, Hewitt.
Substitutes not used: Lewington, Okuonghae, Eastmond, Gordon, Bonne, Szmodics.
Attendance: 3,303 (230 away).