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.
Striker Danny Graham had the best chances to add to Hull's tally - missing a yawning net in the sixth minute and heading straight at Joe Lewis deep in added time - but Bruce is not focused on the Sunderland loannee.
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.
"We have to improve on that. As a team we have to chip in, not just the strikers."
Hull went into the match with three defenders but no outright strikers on the bench, leaving George Boyd as their most attacking substitute.
That says something about the current standing of Matty Fryatt and Nick Proschwitz, who are both available to leave on loan, and left Bruce eager for summer signing Yannick Sagbo to return from suspension.
The Ivorian was sent off for an attempted headbutt on his home debut against Norwich but is available for next week's meeting with Newcastle.
"Sagbo is back, which is good because that gives us another bit of firepower and we haven't really seen him yet," he added.
Cardiff boss Malky Mackay came away reasonably content with his side's efforts, especially given the number of air miles his men had collected in the previous 10 days.
Nine of his players were called away on international duty, a result of squad strengthening since promotion from the Championship, with two - Craig Bellamy and David Marshall - missing the trip to Hull after picking up injuries.
Others, such as Gary Medel and Kim Bo-kyung, came back from gruelling trips to Chile and South Korea to put in solid displays.
"They (Bellamy and Marshall) are key players for us and we lost the two guys: that is the flip side of having top-quality footballers," said Mackay.
"We had three or four who had been on planes, trains and automobiles to get here for the game and at times I thought that showed.
"But it was probably a fair point for both teams, we both tried to go and win it.
"There were two teams going hard at it and it proved to be a tough game, so it was a well deserved point for both teams."