The Hull manager saw his side pick up their fourth point in four matches with a 1-1 home draw over Cardiff City on Saturday.
And Bruce has called on his team to support the strikers if they are to start turning leads into wins before a shortage of points becomes a problem.
"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 had three defenders on the bench for their clash with another of last season's promoted sides with George Boyd their most attacking substitute.
And Bruce is eager to welcome Ivory Coast striker Yannick Sagbo back from suspension as he prepares Hull for their away fixture against his hometown club, Newcastle United
"Sagbo is back, which is good because that gives us another bit of firepower and we haven't really seen him yet," he said.