The Tigers banked their fourth point of the season in as many matches with Saturday's 1-1 draw at home to Cardiff.
It was a fixture Bruce had targeted as a potential win but although things began well with defender Curtis Davies nodding home Tom Huddlestone's cross in the 40th minute, the Bluedbirds always looked likely to equalise.
They did so just before the hour mark, with Peter Whittingham putting the finishing touch on a flowing passing move.
Indeed, Davies' goal is Hull's only one from open play to date and Bruce can track the issue back to last year's promotion campaign when Graham was not even at the KC Stadium.
"At this level if you don't take your chances it's tough," he said.
"Last year it was our Achilles heel too...the number of times I sat here (with a 1-0) and we could have had two, three, four goals.
"It's got to be a concern because we created really good chances. It leaves a bad taste in your mouth.
"On another day we would quite easily have won the game but at this level you don't get chances as good as the ones we had too frequently.
- Sports & Recreation
- Curtis Davies
- Tom Huddlestone
- Peter Whittingham
- Danny Graham