Gary McSheffrey put City in front from the penalty spot after 37 minutes at the Ricoh Arena on Saturday after he was felled by Barry Roche when attempting to go around the Shrimpers goalkeeper.
Captain Carl Baker doubled the lead 17 seconds into the second half with a curling effort against his former club and Richard Wood thought he had made it 3-0, only to see his effort ruled out for offside.
Kevin Ellison scored to bring the visitors back into it with 20 minutes to play but Coventry held on comfortably in the end.
However, Robins felt the victory could, and should, have been more convincing.
"The disappointment for me was that we had a goal chalked off again that was perfectly good," said the City boss. "It's the second time in two games at home, and if we had that it would have killed the game. But as usual we fail to do something that gives them an opportunity.
"It's about defensive responsibility and getting into position quicker than we did do because we ambled back in. Those are the things that teams that win things do well and consistently, and that's the negative.
"The positives are that we have lost two or three players for this game and two or three came in and gave a good account of themselves."
Robins added: "Initially we struggled to get on the ball and play the game we wanted to because they were keeping possession so well until we tweaked it slightly and got into the ascendancy and played some decent football.
"I thought some of the football was excellent from both sides, us particularly, but I still want more."
