The England striker missed a great chance to put the Black Cats in front when one-on-one with Paul Robinson, and the visitors could not break their opponents down, despite playing against 10 men following the 45th-minute sending off of Christopher Samba.
"We can't keep relying on Benty to score us a goal," Bruce said on Sky Sports 1.
"We've got to come up with some goals from someone else. We should be taking some of the chances we've created."
Rovers boss Sam Allardyce had no complaints with Samba's dismissal for bringing down Danny Welbeck just before the Black Cats forward could burst into the box.
"Obviously we can't criticise the referee for that. He's through on goal, we can just be very thankful the assistant referee saw it was outside the box," said Allardyce.
He added: "We deserved the point we got. It's a great point in the end."
Allardyce also launched a defence of his team's style of football in the wake of recent comments by Danny Murphy.
Fulham captain Murphy caused a storm when he pointed the finger of blame at Allardyce, Mick McCarthy and Tony Pulis for the recent rash of dangerous tackles in the Barclays Premier League.
Murphy has since insisted his comments were "blown out of all proportion", but Allardyce said: "Danny didn't need to mention any of the teams he mentioned.
"We've got one of the best disciplinary records in the Premier League at the moment. That would have changed today because we got Chris Samba sent off but it was not through foul play or a dangerous tackle.
"We're getting a perception we're a long-ball team and we're dirty but that's not true."