Kagawa: I need to improve
He told national newspapers: "I have to take this like some kind of message (from the manager).
"I need to improve more and more, or I cannot survive at this club.
"I have to take this in a positive way and keep trying to do my best."
The West Brom clash was Kagawa's first league start of the season, although he did star in the Champions League win over Bayer Leverkusen, and he feels he could have been of use if he had stayed on against the Baggies.
"I thought that I would have been able to find some space to create the chances in the second half," he added.
"In that sense I was disappointed. Sure, I wasn't involved that much. I didn't touch the ball enough but I was trying to be patient so I didn't feel that bad."