The Spurs chief made the 23-year-old Internacional striker his main transfer target during last month's transfer window, but failed to get him in at White Hart Lane before Thursday's 11pm deadline.
It leaves Villas-Boas short on numbers in attack for the remainder of the season with Jermain Defoe the only recognised forward at the club given that Emmanuel Adebayor is still away with Togo on African Nations Cup duty.
Villas-Boas also defended the club's stance over their reluctance to break the bank in order to sign Damiao after Internacional claimed their £13million did not meet their valuation for the player, who has 14 caps for Brazil and was top scorer at the London Olympics last summer.
"We've approached this market very sensibly," he 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."
On the possibility of making another bid to sign Damiao in the summer, Villas-Boas added: "No I don't think (it will happen in the summer).
"It's probably finished now."