A 2-2 draw on the night in Switzerland saw the teams finish the tie 4-4 on aggregate, but Tom Huddlestone and Emmanuel Adebayor both failed to convert their penalties as Spurs went down 4-1 in a shootout.
"My first thoughts are for the players, they set a great example for the country," Villas-Boas is quoted as saying by BBC Sport. "The way they approached the competition, playing every Thursday and Sunday.
"They showed the country it is possible to approach it in a different way. I will cherish this and so should the players, we made the country feel different about the competition.
"It has seen most of the English teams change their approach to the competition and now it means a lot. We set the standard for the future. Next time we will go better as it could not have gone worse tonight."
Tottenham return to Premier League action on April 21 when they take on champions Manchester City at White Hart Lane.