Spurs continue their journey thanks to Emmanuel Adebayor's away goal.
Villas-Boas said: "We set out today to try and get a goal away that would put us in an extremely confident position.
"I think today what happened to us was a bit like what happened to Inter in London.
"They are not as bad as their performance in London and we're not as a bad as the performance we showed today.
"There are still lots of positives in an evening like this because the desire to reach the last eight of the competition was always there from the players, even in extra-time, which is an excellent sign for us.
"I think the organisation wasn't there because their mind wasn't there. Every goal for Inter Milan was a boost of motivation for them and a knife in the back for us.
"We had a lot of problems in our organisation, which they did extremely well [to exploit] and is why we had a very, very hard game."