The Sky Blues had the better of a tight contest and came closest to finding a winner when a 25-yard strike by Jacob Murphy hit the post after the break.
Gillingham had started brightly with Dominic Samuel wasting a good opening when he slipped at the vital moment.
Gael Bigirimana also went close with a curling shot for City, who dropped to 11th, nine points off the play-offs.
The Gills are now 10 points off top spot following Wigan's win over Shrewsbury, but they have a game in hand on the Latics and second-placed Burton.
Covnetry City boss Tony Mowbray told BBC Coventry & Warwickshire:
"I think late on we should have won that. It was alright, although for most of it was a pretty poor football match.
"We had a gameplan and it nearly paid off.  We nearly came away with a 1-0 victory but it wasn't to be."

The Northampton skipper will not be able to play until 14 May, meaning he is free to take part in England's June tour to South Africa if selected.
Ireland flanker Ferris drew attention to the incident during England's 30-9 Six Nations victory on 17 March, but it was not spotted by referee Nigel Owens.
"I am disappointed by the result," said Hartley, who may decide to appeal.
"I will wait for the written judgment as to how the panel came to their conclusion.
"I now have to put it behind me and focus on supporting Saints in training and off the field."
Hartley has been ruled out of the rest of the regular domestic season but he could return if Saints reach the Premiership final on 26 May.
The lowest suspension for biting is 12 weeks, with a maximum sanction of four years.
But an independent Six Nations disciplinary committee decided Hartley's case was worthy of a lesser punishment after Tuesday's hearing.
"The offence merited a low entry point in the International Rugby Board's table of sanctions and allowed mitigation of four weeks," said a statement released by the committee.
The panel listened to evidence from both Hartley and Ferris, who spoke via videolink, while England forwards coach Graham Rowntree and Northampton director of rugby Jim Mallinder also represented their player.
Rowntree said: "It is unfortunate for Dylan and Northampton, especially as he was in good form during the Six Nations, and he has developed as a player and a leader.
"However, we are looking forward to him being available for the tour to South Africa."
Mallinder added: "We are disappointed that Dylan has been suspended, especially at a crucial part of the season."
It is the second time Hartley has received a lengthy suspension from the game. He received a six-month ban for eye gouging while playing for Northampton against Wasps in 2007.
Mid-table Coventry City earned a point from a drab match as Gillingham missed the chance to go third in League One.
[NEXT_CONCEPT]
England hooker Dylan Hartley has been handed an eight-week ban for biting the finger of Ireland's Stephen Ferris.