Spurs go to Old Trafford on Saturday evening having not won there against the Red Devils since 1989.
"It would make us very proud to go there and get a win that would shorten the distance to the top," Villas-Boas told reporters.
"We can't run away from our responsibilities. The statistics are there. We hope to break them one day and hopefully it will be on Saturday."
Tottenham are currently eighth in the Premier League table.