The win has kept Chelsea third in the Premier League table, but they have closed the gap on second-placed United to one point.
"It's important for us to get three points, particularly on a day where two title contenders played against each other," said Villas-Boas.
"We have done nothing else than our responsibilities in winning the games that we have won at home. We have not done anything special.
"We just have to continue to win until we find a position of comfort at the top of the Premier League, because that's what we want."
The Blues host Belgian side Genk in the Champions League on Wednesday.