Spurs have moved up to third in the standings after winning four games.
"It's been an excellent December for us and we've managed to put ourselves in the kind of position that we want to be," said Villas-Boas.
"We sit third in the league, but it is where we finish at the end of the season that matters."
The Dutchman found the net five times as United won five of their six Premier League games during the month.
Van Persie told the United website: "It was a big month for us. You have certain periods during a season when it goes your way and December was one of those periods."