Villas-Boas guided his team to their first win at Old Trafford since 1989, achieving a feat that Spurs' previous ten managers had not.
The 34-year-old was visibly delighted with the win at the final whistle, and he believes that his players deserve to feel proud of themselves.
"We were tremendous today, the players put in the effort and intensity to get a result," he said.
"The first half was totally different from the second but we can be proud of each other.
"It was an electric first 15 minutes of the second half but you can see from the desire to hold on to such a historic result that we can count on each other to do big things."
Tottenham's next league match comes next Sunday when they play host to Aston Villa.