The Germany international was satisfied with how his first game for the Bundesliga champions went, but he also insisted that he still has plenty of work to do
The 21-year-old, who joined Bayern from Borussia Dortmund this summer, had spent the past few months on the sidelines due to injury.
However, the Germany international featured for 30 minutes at the weekend and netted twice to help his side to victory.
"It was only a friendly game, but still something quite special for me," Gotze was quoted as saying by TZ.
"Could I start against Frankfurt this week? No. I'm still missing something, I have some catching up to do in the next three to four weeks.
"My debut could have gone worse, though... I am happy with how things went. I just want to keep on training with the team to gain a bit of rhythm."
Bayern team-mate Franck Ribery was also thrilled with the attacking midfielder's substitute cameo and is looking forward to playing alongside Gotze more often.
"It was good fun to play alongside Mario," he said. "It was clear to see that he really missed playing football. We will have plenty of fun together this term."