The Chelsea boss insisted prior to kick-off the Brazil international's omission was a 'tactical decision', with Andreas Christensen lining up in the centre of defence and Ethan Ampadu on the bench.
But after seeing Alvaro Morata score the only goal of the game at Stamford Bridge, Conte was more forthcoming with his assessment of the situation.
"[David Luiz] can get on with the other players or he sits in the stand," he told Sky Sports. "If he deserves to play, he plays; if not, he's in the stand."
When directly asked if David Luiz has a future at Chelsea, Conte replied: "I don't know."
In his post-match news conference, Conte attempted to clarify the state of affairs by reverting to his earlier position that David Luiz had been dropped for tactical reasons.
He added: "It's only a tactical decision, only a tactical decision, only a tactical decision. It's normal. This can happen to every one of my players, if I see that they are not in good form. It's normal."
Asked if he meant to sound uncertain about David Luiz's future at the club in the previous interview, Conte appeared to go back on his comments.
"No ... [checks with press officer]. I think that I have a squad. I have a squad with 16 senior players, and five young players. I have these players, and then I repeat I have to make the best decision for the team. I try to do this," he said.
There were plenty of positives for the reigning champions to take from the victory, though, with Morata ending a six-game goal drought to the delight of his manager.
"He showed a great personality, showed he's very strong," Conte said. "He played a great game.
"There is a little disappointment because he could have scored more, but remember this is the first season he has played as a number nine.
"He's a young player but it's great for his confidence, for the confidence of Chelsea. I think he played a great game."
Chelsea are still nine points behind Premier League leaders Manchester City, however, and Conte acknowledges it will be tough to muster a genuine title challenge.
"It will be very difficult because City are having an impressive run, winning games," he said.
"But I think we must look at ourselves and play with the same spirit as [against United] and try to give our best for ourselves and our fans."