The North London club were thought to be closing in on the Brazilian's signature on deadline day but failed to meet the asking price.
"We've approached this market very sensibly," Sky Sports News quotes Villas-Boas as saying. "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."
Reports have claimed that Spurs offered a bid in the region of £20m for the forward, who has racked up 14 caps for Brazil.