In the second, Elliott and Burgess were both denied with headers as City piled on the pressure.
Yeovil's Hugo Rodrigues hit the top of the goal with a header after Paul Musselwhite failed to collect, but that was the closest the visitors came to scoring.
Then it was back to the Yeovil end, and they survived a scare as the ball went across their goalmouth.
Stuart Green was furious after being denied a penalty as he was bundled down just inside the box a minute later.
Chris Weale made another great save from Jason Price's back post header, while Elliott missed further chances.
Ian Ashbee hit a superb 20-yard volley but was again denied by the fingertips of Weale.
As substitute Ryan France's shot went across the face of goal in the 90th minute, City knew that it just wouldn't go in, and had to settle for a point.
City line-up (4-4-2): Musselwhite; Hinds, Joseph, Delaney, Dawson; Price, Green, Ashbee, Elliott; Burgess (France 72), Forrester (Webb 87).
Un-used subs: Whittle, Holt, Keates.