Thomas Muller admitted he was "a little bit lucky" with his opener against Olympiakos on Wednesday but Pep Guardiola said there was nothing fortunate about the 3-0 victory.
Muller broke Olympiakos' resistance at the Karaiskakis Stadium on 52 minutes when his cross from the right wing caught out the hosts' goalkeeper, Roberto.
Mario Gotze then made the game safe on 89 minutes before Muller completed the scoring from the penalty spot in injury time.
"We had difficulties in attack today because Olympiakos left us no space in the middle," Muller told reporters after the game. "We're delighted to come away from here with three points. Winning the opening match is always important."
Asked about his opener, Muller admitted he had been attempting a cross for Robert Lewandowski, adding: "I have to be honest and say the ball bobbled slightly before the opening goal. It was a little bit lucky but very important for us."
Bayern boss Guardiola, though, said his side's victory owed nothing to fortune.
"We were totally in control," he said. "They barely created anything and we made enough chances to win it. The second goal from Mario wrapped it up. All credit to my players. It's a first step and I'm very, very pleased."
Gotze, who missed Saturday's 2-1 win over Augsburg with a minor injury, scored 10 minutes after coming off the bench as the third and final substitute in Greece.
Explaining his decision not to start the Germany international, Guardiola told Sky: "He's a top player, but I also have Robert Lewandowski, Thomas Muller and many others. Mario had some [injury related] difficulties in our match against Augsburg.
"He will win a lot of minutes here, because he's a super person and super lad. I want the best for Mario, and I am here to help. I understand that he's disappointed.
"It's a long season. Mario has outstanding quality and a great attitude. I love Mario Gotze. I am sorry."