Jackson, 24, joined the German champions on a season-long loan from Chelsea for a reported €16.5 million (£14m/$19m) fee, which includes a €65m (£54m/$71m) purchase option. However, the Senegalese international has failed to score in his first six Bundesliga appearances, leading to questions over his suitability.
Despite the mounting external pressure, Kompany was unequivocal in his support, stating he has a "completely different opinion" to the public and explaining his reasoning.
"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."