Barnet's works, while remaining universal, reference his own personal history complete with images of his wife, his daughter, and their family pets. As James Thomas Flexner wrote, Barnet’s work “makes us experience the interplay between the personal and the universal.” While remaining representational, the simple elegance of the figures and their flat surfaces reflect his exploration with abstraction. He was a key figure in the New York movement called Indian Space Painting, artists who based their abstract and semi-abstract work on Native American art. For many years he pursued abstraction in painting, then a fashionable trend in the USA. His later work returned to figurative painting. He is probably best known for his enigmatic portraits of family, made from the 1970s onwards, notable the Silent Seasons series. However, his earlier works maintain an edginess and brooding contemplation that is even more remarkable when compared with the more placid and pretty works which followed his second marriage.

His works have entered virtually every major public collection in the United States, including, the National Gallery of Art, the Metropolitan Museum of Art, the Whitney Museum of American Art, the Museum of Modern Art, New York, the Museum of Fine Arts, Boston, the Philadelphia Museum of Art, The Jewish Museum, and the San Francisco Museum of Modern Art. He has been the subject of over eighty solo exhibitions held at the Virginia Museum of Fine Arts, the Museum of American Art of the Pennsylvania Academy of Fine Arts, the National Academy of Design Museum, the National Museum of American Art, Montclair Art Museum, and the Boca Raton Museum of Art among others, including the Crystal Bridges Museum of American Art in Arkansas.

 A longtime resident of the National Arts Club, Barnet died in New York City on November 13, 2012, at the age of 101.