Reading made three bids for the midfielder on deadline day, with Brian McDermott determined to return Sigurdsson to the club in which he first made his name in English football.
Spurs were unwilling to do business, though, which each approach knocked back.
Sigurdsson has struggled to hold down a regular role since moving to White Hart Lane last summer, but Villas-Boas still considers him to be an important part of the senior set-up.
He said: "Obviously he's a player that means a lot to Reading.
"But he's a player that we rate very highly, we brought him here after his amazing contribution (on loan) for Swansea last year and he's a player we have high expectations for.
"Probably this season, at the moment, he is not going to the level he wants, but he's a player that we believe a lot in, and in his future here.
"We couldn't allow him to leave."