Having last won the Champions League title in 2001, Bayern begin their Group A campaign at Spain's Villarreal on Wednesday.
Tough tasks lie ahead as Bayern face German title-rivals Schalke 04 and Bayer Leverkusen over the next two weekends in the Bundesliga before hosting Manchester City at the Allianz Arena on September 27 in the Champions League.
"We know we'll have to keep on improving, because we have a packed and intense programme over the next few weeks," said Heynckes.
Bayern striker Mario Gomez, who scored four goals, and midfielder Franck Ribery, two, shone in Saturday's rout in Munich while replacement Nils Petersen scored the seventh just before the final whistle.
The rout leaves Bayern top of the league and with just over a month gone of the new season, they already have a goal difference of 15.
Second-placed Werder Bremen are level with Munich on 12 points after beating neighbours Hamburg as ex-Chelsea striker Claudio Pizarro scored both goals in their 2-0 home win.
On Sunday, Nuremberg ran out 2-1 winners in a bad-tempered game which saw both sides finish with ten men.
Both Nuremberg goals came from penalties as Belgium midfielder Timmy Simons slotted spot kicks on 31 and 35 minutes, while Cologne's Morocco striker Adil Chihi kept his side in touch with a 39th-minute strike.
The result leaves Nuremberg seventh and Cologne 14th in the table.
On Saturday, defending champions Borussia Dortmund suffered a shock 2-1 defeat at home to Hertha Berlin as they prepare for Tuesday's visit of Premier League side Arsenal in the Champions League.
This was Dortmund's second defeat in four league games and leaves Jurgen Klopp's side 11th in the table and puts Berlin eighth.
Borussia Moenchengladbach, who only avoided relegation last season by the skin of their teeth, maintained their great start to the season with a 1-0 win at home to Kaiserlautern to go third.
Stuttgart enjoyed a comfortable 3-0 win at home to Hanover, while Hoffenheim hammered Mainz 4-0.
On Friday, Bayer Leverkusen warmed up for Tuesday's trip to Chelsea in the Champions League with a 4-1 win over Augsburg which puts them fourth in the table.
On Sunday night, Schalke 04 are at 2009 Germans champions Wolfsburg.