Spurs took a 10th minute lead through ex-Gunners striker Emmanuel Adebayor before he was sent off for a reckless challenge on Santi Cazorla eight minutes later.
That opened the door for Arsenal to fight back against their North London rivals with Per Mertesacker, Lukas Podolski, Olivier Giroud, Cazorla and Theo Walcott getting themselves on the scoresheet along with Spurs ace Gareth Bale.
Despite the heavy defeat, Villas-Boas felt his side did well even though they had a man disadvantage and feels it could have been a different story if Adebayor avoided his poor challenge.
"I think the sending-off determined the game, but the referee made the right decision. Players want to dispute the ball, there was no intention to do any harm,” he said.
"I'm very, very proud of the team. We had chances for 4-3 and if it had gone to only a one-goal difference, I think we could have gone all the way.
"We had the ambition and desire and I am extremely proud of the team."