Barnet influenced a generation of artists, including James Rosenquist, Knox Martin, Paul Jenkins and Cy Twombly. Barnet continued his love of teaching with positions at the Cooper Union, at Yale University, and at the Pennsylvania Academy of Fine Arts. He had three sons, Peter, Richard, and Todd Barnet, by his first wife Mary Sinclair. Barnet later married Elena Barnet, with whom he had a daughter, Ona Barnet.
