Alberto Zaccheroni's men took the lead versus Ivory Coast on Saturday through a first-half goal from Keisuke Honda.
However, Japan failed to build on that advantage and slipped to defeat in their Group C opener as Wilfried Bony and Gervinho found the net for Ivory Coast.
The setback leaves Japan in need of a positive result against Greece in Natal on Thursday.
And Kagawa feels an extra responsibility to perform well after expressing disappointment with his showing in the first game.
"We have to win it (the second game) and we cannot look back on the last game because there is no time for that," Kagawa said.
"After the game, I blamed myself. Now all we can do is just prepare for the next game.
"The fact that we did not achieve a good result in the first game was down to my ability. All I can do is to prepare well for the next game."
