A fundamental prerequisite for the implementation of organic semiconductors (OSCs) in spintronics devices is the still missing basic knowledge about spin injection and transport in OSCs. Here, we consider a model system consisting of a high-quality interface between the ferromagnet cobalt and the OSC copper phthalocyanine (CuPc). We focus on interfacial effects on spin injection and on the spin transport properties of CuPc. Using spin-resolved two-photon photoemission, we have measured directly and in situ the efficiency of spin injection at the cobalt-CuPc interface. We report a spin injection efficiency of 85-90% for injection into unoccupied molecular orbitals of CuPc. Moreover, we estimate an electron inelastic mean free path in CuPc in the range of 1nm and a 10-30 times higher quasi-elastic spin-flip length. We demonstrate that quasi-elastic spin-flip processes with energy loss <= 200 meV are the dominant microscopic mechanism limiting the spin diffusion length in CuPc.