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 night'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 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."
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