The 28-year-old Germany international was a key figure in the Bayern squad which claimed the league, DFB-Pokal and Champions League trophies.
Schweinsteiger, who has spent his whole senior career with the Bavarian club, knows the arrival of new coach Pep Guardiola heralds another new chapter.
Pictured with the 13 trophies he has won in his career, Schweinsteiger told Germany's Bild am Sonntag newspaper: "To see them all grouped together is really, really nice - it makes me hungrier than ever.
"My title hunger has increased by winning the title, not decreased.
"It is certainly very good for the self-confidence. We will go into the new season with our heads held high.
"We have a world-class coach arriving and I'm definitely excited, but we start all over again under Pep Guardiola and the past counts for little."
Schweinsteiger also suggested that one successful season, coming as it did three years after Bayern last picked up a trophy, does not mean they are the best side in Europe.
"In my eyes, Barcelona are still number one in Europe," he said, in spite of Bayern's 7-0 aggregate victory over the Catalans in the semi-finals of the Champions League.
"They have been incredibly consistent in Europe for the past six years. We cannot claim just after winning one big title that we are now number one in Europe."
Schweinsteiger did reveal that missing out in the European final to Chelsea a year ago, especially on home soil, provided the spark which ignited such a successful last 12 months.
"I can still remember all of the sad faces of the players in the dressing room," he said.
"From that we developed spirit, which we have benefited from this season and we are going to benefit even more from it in future.
"We know each other better now and we have built up mechanisms, like Barcelona, where everything works in perfect harmony.
"One cog turns the other. We are going to see even more of that with Bayern in future."