"That was very important," Villas-Boas told BBC Sport. "It meant a lot for our fans - we wanted to get this one over Arsenal and create a distance between us.
"We will try and push on and qualify for the Champions League. It's not over until the last game of the season.
"It's a good, important win against a top club who are fighting for the same objectives."
The victory has seen Tottenham open up a seven-point gap over fifth-placed Arsenal.