Steve Cooper's struggling Forest side, who are now without a win in 10 consecutive league games, are third from bottom, level on 27 points with 17th-placed Everton.
Reuters reports Antony scored in the 32nd minute at the City Ground, sliding in to poke home a rebound after goalkeeper Keylor Navas's brilliant save kept out Anthony Martial's shot.
Dalot found the net in the 76th minute, scoring his first Premier League goal in his 100th appearance for United, running onto a pinpoint through ball from Antony.