Bayern qualified 3-2 on aggregate in their playoff but only after struggling against the Scots, who had the better chances and took the lead in the 63rd minute through Nicolas Kuhn, a former Bayern reserve player.
The hosts needed a last-gasp goal from Alphonso Davies to seal their spot in the next round following last week's 2-1 victory in Glasgow.
Bundesliga leaders Bayern were in Celtic last week before travelling to reigning champions Bayer Leverkusen on Saturday for the Bundesliga's top-of-the-table clash where they played out a goalless draw.
"We always talked about how many matches we have in six days," Kompany told a press conference. "It is simple. The first half could have been better, the second half was good. We had chances and could have scored more goals.
"It is not easy to get through such a programme. You have to see it in this context. Our goal is for performance and results to match, starting Sunday."
Bayern, who have an eight-point lead over second-placed Leverkusen in the Bundesliga, could be without Harry Kane on Sunday at home to Eintracht Frankfurt, who are five points further back in third, with the striker taken off at halftime.
"We were in Glasgow on Wednesday. Then Leverkusen. Big energy output. It is normal after the second game to take an extra day to recover," Kompany said, adding that Kane's knock to the face in the game at Leverkusen had not been serious.
"He (Kane) gave the thumbs up this morning,. But during the game he felt like he wasn't fully able to help the team. We did not want to take the extra risk. How long or if he is injured, I still don't know."