Two-dimensional turbulent flows can be strongly affected by the interaction with the three-dimensional environment in which they are embedded. This interaction is often frictional, and can be modeled by means of a linear damping term in the equation of motion. In both experiments and numerical simulations it has been observed that, due to the presence of friction, the kinetic energy spectrum deviates from the classical Kraichnan prediction k^(-3). We discuss the high-friction asymptotics, deriving explicit expressions for the spectral slope and for the scaling exponents of vorticity structure functions.