Smith initially joined Millwall on loan from Tottenham Hotspur in the autumn before extending his deal until the end of the season last week.
However, before the 21-year-old signed his extension, reports suggested Wigan Athletic were keen to hand Smith the chance to play in the top flight.
The right-back, who has made two appearances for Spurs, declined that opportunity in order to be guaranteed regular first-team football with Millwall.
"I wanted to stay here because I am playing every week," said Smith.
"I am still young and want to keep on improving, and I can only do that by playing.
"We talked about a move to a Premier League club but I wasn't guaranteed to play and I don't want to go anywhere just to sit on the bench."