Penalties proved the difference in Switzerland after the match finished 2-2 on the night and 4-4 on aggregate, with Spurs losing the shootout 4-1 after Tom Huddlestone and Emmanuel Adebayor failed from the spot.
It ends what has been a rollercoaster European campaign for Villas-Boas' side and the Portuguese was left understandably frustrated with their from the competition he won with Porto, but proud of the way they equipped themselves.
"Obviously we are extremely disappointed," Villas-Boas said. "We did ever so well to cancel the two goals from White Hart Lane.
"I think we played a better game this time round. Both teams were very attacking so compliments to both, with eight goals in two ties.
"In penalties anything can happen and it wasn't our day - it's part of the game.
"I think within all of this disappointment we are extremely happy to set a great standard and a great example this season for English football for the way we approach this competition.
"It's not up to me to brag about it, but I would like to compliment the players because changing the mentality towards the competition from one season to another is extremely difficult. They have done it like heroes, played like heroes.
"It was never an excuse for the way we played in the Premier League and I think that example has stuck so much that it has changed the way some other English clubs approached the competition and spoke about the competition.
"I am proud of the players because, for me, they are like heroes for the way they've done it. We're extremely disappointed to go out to Basel but at the same it is a great honour to have managed them in the competition."
- Sports & Recreation
- Emmanuel Adebayor
- Tom Huddlestone