The 21-year-old joined Millwall on a loan deal at the beginning of the season, with the understanding that he would return to his parent club in January.
However, the right-back has claimed that the opportunity of first-team football played a major role in convincing him to remain with the Championship outfit until the end of the season.
"I wanted to stay here because I am playing every week. I am still young and want to keep on improving, and I can only do that by playing," he told reporters.
"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."
Smith has made two first-team appearances for Spurs.