Last year, the German club got into a tight corner in the group stage of the competition and had to win their final two matches to escape an early exit.
They made it through and eventually lost to Inter Milan in the final.
"Against Roma we need to make sure we avoid making the group phase into a tension-filled affair like last season," striker Thomas Muller told reporters on Monday.
"There does not seem to be a logical explanation for this (lack of goals)," said Muller.
"We definitely did not have a perfect pre-season training. But this needs to change now," Muller said.
Bayern will also be without playmaker Franck Ribery, serving out the remainder of a three-match ban following a straight red card in last season's Champions League semi-final against Olympique Lyon.
Claudio Ranieri's Roma side were hammered 5-1 at Cagliari on Saturday in their second Serie A game. They fell apart after Nicolas Burdisso, the former Inter defender whom they had worked all summer to sign, gave away a penalty and was sent off midway through the first half.
Captain Francesco Totti was surprisingly substituted for Burdisso's younger brother and defender Guillermo to help them cope with 10 men but the ploy failed spectacularly.
"We have to start over with determination and look each other in the eyes to find some positives," Ranieri told reporters.
Roma, last season's Serie A runners-up, are in the process of being sold after racking up huge debts and their transfer deals were limited during the August window.
