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.
Villas-Boas said: "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."
He added: "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 Basle but at the same it is a great honour to have managed them in the competition."
It was a fittingly dramatic end to what has been a tumultuous tournament for Spurs, who took the lead at St Jakob-Park through Clint Dempsey.
Basle hit back through Mohamed Salah and Aleksandr Dragovic, only for Dempsey to take the game to extra time with his second of the night.
Spurs did well considering they had to do without Jan Vertonghen after his sending off late in regulation time, with penalties eventually proving their undoing.
- Sports & Recreation
- Emmanuel Adebayor
- Tom Huddlestone