Spurs lost 4-1 after extra time on the night, but advanced thanks to the away goals rule.
Antonio Cassano struck twice, either side of a Rodrigo Palacio effort, to level the aggregate score after 90 minutes, but Emmanuel Adebayor scored the vital away goal.
Ricardo Alvarez set up a tense finish, but the Londoners held firm to book their spot in the quarter-finals.
AVB was happy to see his side advance and believes that they have learnt much about European football throughout the tie:
“Tonight we suffered what Inter did in London. When the mind isn’t working, everything becomes a catastrophe,” he told Sky Sports Italia.
“I think every time Inter scored, they felt stronger and it was like a knife wound for us. We really struggled a lot.
“The players did brilliantly to go through. I could not be afraid, because I felt the team was going towards its objective.
“However, this was a real lesson for us and we must learn from it if we are to become great in Europe.”
Gareth Bale was unavailable the game at the San Siro through suspension, after picking up a yellow card in the first-leg.
Villas-Boas believes that Spurs missed their talisman, but also confessed that Inter were in the same position last week:
“Bale is an important and decisive players, so yes he was missed, just as Rodrigo Palacio was missed by Inter in the first half at White Hart Lane.”
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