Concept of Karma in Bhagwad Gita and Buddhism

In Hinduism, there are many philosophies developed regarding the concept of God and afterlife, and they all give their own interpretations. Regarding the Karmic approach, the main book that gives insight about that is the Bhagwad Gita. - The main concept that arises from it is that no man can exist without doing any karma **(Knowingly or Unknowingly)** and hence krishna says that "any Karma without attachment is the right way to not get bounded by your karmic effects". - Whereas Buddhism says, any act of Karma whether good or bad is bound to create attachment so the best way is to not indulge in any karma altogether. As a man can`t live without doing karma, and this will result in karmic debt, isn't the salvation of a person (Nirvana) infeasible by this approach? Are Buddhism and Bhagwad Gita on different pages, regarding the concept of karma?