Goals from in-form Gareth Bale, Gylfi Sigurdsson and Jan Vertonghen secured a vital victory to take to Italy for the return leg next week with Spurs in charge for a large portion of the game.
Inter missed a good chance in both halves but were underwhelming for most of the game and Villas-Boas believes his side were deserving of the result.
"It was a very good performance and a great night of European football for us," he said.
"We really felt that at half-time we could have gone further - there were some important moments of the game for Inter Milan too but we had so many opportunities - we really deserved to win.
"Unfortunately for us it doesn't mean we are through yet, it is a difficult place to go and I just hope we can do enough to qualify.
"I think the result is what it is and it is well deserving for Tottenham and still prestigious."
- Sports & Recreation
- Gylfi Sigurdsson
- Jan Vertonghen