Villas-Boas made Damiao his top January transfer target but, despite a last-ditch attempt, Spurs failed to land the 23-year-old before Thursday's 11pm deadline.
Chairman Daniel Levy's failure to sign Damiao means Jermain Defoe and Emmanuel Adebayor will be Tottenham's only recognised senior strikers for the rest of the campaign, and the latter may not be available for up to another two weeks as he is away at the African Nations Cup.
Internacional claimed last night they did not let Damiao leave for White Hart Lane because Spurs' offer, reported to be £13million, did not meet their valuation of a player who has 14 caps for Brazil and was top scorer at the Olympics.
Villas-Boas admits being left with two strikers is a "risk", but brushed off suggestions the club should have pushed the boat out to sign Damiao.
"We've approached this market very sensibly," the Tottenham manager told a press conference.
"I've said in our conversations that if (the Damiao bid) was going to go out of proportion, we would step out of it.
"We have made it public before that he is a player that we chase, but we couldn't agree on the full conditions so we've moved on."
Tottenham, who have a club partnership with Internacional, were expected to renew their interest in Damiao this summer, but Villas-Boas claims that is now unlikely.
"No I don't think (it will happen in the summer)," Villas-Boas said. "It's probably finished now."
Levy has become famed for his love of a last-minute deal in the window. He landed Rafael van der Vaart in the dying minutes of the summer window in 2010 and he left it late to capture Clint Dempsey last August.
But his failure to land Villas-Boas' top two targets in the past two windows - Damiao and Porto's Joao Moutinho - has left some fans unhappy.
Villas-Boas, who added Zeki Fryers and Lewis Holtby to his ranks last month, remains convinced his squad can finish in the top four this season, however.
"The fans' concerns are made by opinion-making and media expectations, so it's a roller coaster and it's more difficult for them to take," the Portuguese said.
"If this window hadn't opened, we sit fourth with the squad that we started the season with and you look pretty comfortable where you are. We are as we stand."
Most of the focus on Spurs on deadline day on Thursday was on departures. Heurelho Gomes, Andros Townsend, and a number of youngsters left on loan while Jermaine Jenas was transferred to QPR.
One player Villas-Boas was unwilling to let go, however, was forward Gylfi Sigurdsson, who was the subject of interest from his former club Reading.
The Iceland international, who snubbed Liverpool to move to Spurs from Hoffenheim last summer, has found it hard to break in to Villas-Boas' first team this season, but Villas-Boas retains full confidence in the player.
"Obviously he's a player that means a lot to Reading," Villas-Boas said.
"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 that we have high expectations for.
"Probably this season at the moment he is not going to the level that 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."
Tottenham are looking to return to winning ways against West Brom on Sunday following a disappointing week in which they drew at Norwich after being knocked out of the FA Cup by Leeds.
"We were very disappointed with the FA Cup exit," Villas-Boas said.
"We wanted to get back to winning ways at Norwich. It was not the result we were looking for.
"We want to get back to winning ways. It has been a while since we won and as this run drags on you become more committed to getting the win."