We report new limits on cosmic neutrino fluxes from the test flight of the Antarctic Impulsive Transient Antenna (ANITA) experiment, which completed an 18.4 day flight of a prototype long-duration balloon payload, called ANITA-lite, in early 2004. We search for impulsive events that could be associated with ultrahigh energy neutrino interactions in the ice and derive limits that constrain several models for ultrahigh energy neutrino fluxes and rule out the long-standing -burst model.