Mark Robins was left disappointed despite seeing his Coventry side take a hard-earned point at Ashton Gate.
The manager rued missed chances, especially in the second half, and felt his side should have gone home with a victory.
Viktor Gyokeres twice broke clear on goal in the second half, only to shoot wide on 48 minutes and have his 64th-minute effort parried by Bristol City goalkeeper Dan Bentley.
Fellow striker Matty Godden had a 50th-minute header cleared off the line and another effort blocked by Rob Atkinson in the closing stages.
Robins said: “We had the best chances of the game and we just needed to be a bit calmer at times.
“I am not going to criticise any individual, but we should have taken the game away from Bristol City at the start of the second half.
“Viktor could have taken another step with his first shot instead of shooting when off balance.
“The second chance he had brought a very good save and as long as he keeps getting into those positions I will have no complaints.
“It's a good point for us and an outstanding clean sheet. We had to defend a lot of crosses and did it really well.
“Bristol City are a dangerous team going forward and I felt we contained them to few clear openings.
“I thought we should have had a penalty for handball in the second half, but in the end we have come away with a draw against very good opponents.”
Bristol City boss Nigel Pearson said: “We put in 40 crosses and it wasn't until Tommy Conway went on as a sub that we got on the end of one.
“Give Coventry credit for defending their box really well. But on another day we would have made our pressure tell.
“It was an honest performance from my team against a Coventry side who are only in their current position because they have played less games than everyone else.
“We needed to keep a clean sheet and it was particularly important as it's the first time we have failed to score in a game this season.”
The home side suffered a blow on 41 minutes when centre-back Kal Naismith limped off to be replaced by midfielder Joe Williams.
“It's a calf injury, but don't know yet how serious it is,” said Pearson. “Andy King showed his experience by dropping into defence and we coped with the change well.
“We don't have a lot of options in central defence, with Tomas Kalas and Timm Klose injured, so hopefully Kal will be okay soon.”
For exclusive stories and all the detailed EFL news you need, subscribe to The Football League Paper website, digital edition, or newspaper from as little as 14p a day.
