Bayern narrowly secured a 3-2 victory against Wolfsburg, courtesy of a late goal from Serge Gnabry, after conceding twice early in the second half last Sunday.
"We observe everything, delve into details to find solutions and strive to create a perfect picture. We performed very well in the first half against Wolfsburg but lost momentum just after halftime," Kompany told reporters on Friday.
"Such lapses often occur due to mistakes. However, we fought back and persevered. The mentality was commendable. We need to address these issues as a team."
Freiburg claimed an impressive 3-1 win against VfB Stuttgart in their first match and Kompany acknowledged that Sunday would be a challenge.
"It’s a difficult game for us but our objective at home at the Allianz Arena is always clear," Kompany said.
Despite injuries to players, including Hiroki Ito and Josip Stanisic, Kompany was unconcerned about the overall squad situation.
"We’re close to having everyone available. I don't want to exert too much pressure. We don't have many worries. I hope we’ll have everyone fit soon," he said.
Kompany said he was excited about the new-format Champions League, where Paris Saint-Germain and Barcelona will be among Bayern's adversaries.
"It feels new and exciting. I'm looking forward to it because it'll be different. You have eight opponents in very different situations. Previously, it was often clear who would advance after four games," Kompany said.
"I’m excited about the fixtures. An away game in Rotterdam is always nice; playing at home against Paris and away in Barcelona. The key is to keep the players fit, then we can relish the games."
