The 23-year-old knows his team must play up to their full potential if they are to defend their Champions League crown
The Bavarians have won four and drawn one from their first five Bundesliga games and have lost just once since the arrival of Pep Guardiola - a 4-2 defeat at the hands of Borussia Dortmund in the DFL Supercup final.
But Kroos insists they have not yet played up to their own high standards, with club director Matthias Sammer publicly declaring the players' efforts have not been good enough.
“Until now we have won our games but perhaps we did not play as good as we could have,” he told reporters.
“This could be a danger in our next games. So Matthias Sammer has every right to give his opinion about our performance on the field.
“We are looking forward to this season a lot. And it is something special to go in this season as defending champions.
“We remember last season which was quite special and now it is the beginning again, something which could be very special again.
“We want to start with a win in this group stage.”
Kroos’ teammate and Bayern goalkeeper Manuel Neuer agreed with the midfielder's claims.
“I think we did not show our best in the first half of the Hannover game but in the second we did much better.
“We should go on playing like this during the next games, starting tomorrow.”
Bayern kick off the Champions League title defence on Tuesday when Russian outfit CSKA Moscow visit the Allianz Arena in a Group D opener. Manchester City and Viktoria Plzen are also in the group.