Marcelo Bielsa's men fell to a 4-2 defeat to the Reds on a frantic New Year's Day clash at the City Ground.
Phillips saw red on the stroke of half-time as a heavy touch saw the 23-year-old lunge into a challenge with Adlene Guedioura with referee Darren England brandishing a straight red card.
United fought back after falling behind after just six minutes following a mistake from Adam Forshaw which allowed Jack Colback to open the scoring.
Despite being down to ten men Leeds turned the game on its head after the break as substitute Jack Clarke and Gjanni Alioski both scored to send the travelling fans wild.
Forest though provided a fightback of their own as they bagged three goals in seven minutes with Colback, Daryl Murphy and Ben Osborn all getting on the scoresheet to seal the points for Aitor Karanka's side.
Phillips though apologised to the Leeds fans and his team-mates following the 4-2 defeat, tweeting: "I apologise to my team mates and our amazing travelling fans for my red card today.
"I mistimed my tackle, I accept responsibility and I will make up for my mistake."
United defender Pontus Jansson later responded to his team-mate, saying: "You are one of the biggest reasons why this team are first in the table and you have been standing up for us every single minute so far so don’t say sorry, we are all behind you!"