The 24-year-old joined on loan from Chelsea at the end of the transfer window for a reported €16.5 million fee, which includes a €65m purchase option.
Jackson has struggled to adapt to life in Bavaria and is yet to score or assist in the Bundesliga, although he’s only started three of his six games.
Bayern legend Lothar Matthaus recently claimed he looks "out of place," a sentiment that Kompany doesn’t seem to agree with.
"He's working very well," Kompany said. "We talked about his integration last week, and it's gone very quickly for him. I know why the question comes up, but I have no problem having a completely different opinion. I'll explain why objectively."
"In the first half against Dortmund, for example, he played an outstanding role, and the same against Pafos. He interpreted the game very quickly, understood what we wanted from him, and also got off to a good start against Club Brugge."
Kompany dismissed the goal-centric criticism as simplistic: "He's a striker; when he scores, we say he's the best.
“When he doesn't score, we say maybe he's not good enough. I'm happy that we have Jackson here; he'll be important for us this season. In terms of his playing ability, he's already where he needs to be, if only the goals would come."