A double from Jan Vertonghen had handed the visitors a 2-1 lead in the second half, but two errors from the Spurs defense allowed Brendan Rodgers' side to earn victory.
Goals from Jan Vertonghen either side of halftime helped Spurs cancel out Luis Suarez's opener but a succession of mistakes from Kyle Walker and Hugo Lloris allowed Stewart Downing to level matters.
After Benoit Assou-Ekotto conceded a late penalty in similarly calamitous circumstances for Steven Gerrard to claim all three points, Villas-Boas bemoaned the Tottenham's misfortune.
"It’s difficult for us to take. We did ever so well to come back into the game first half and then started brightly the second half," he told reporters. "I think we had control of the game until we lost it. It was more down to a couple of mistakes rather than to Liverpool’s merit, although they fought very, very hard and pressed us hard and in the end they deserved [a result].
"But it’s a pity that we lost control of the game when things looked to be going our way. Probably the [Gylfi] Sigurdsson chance for 3-1 that hits the post could be the moment of the game because that would probably mean three points for us."
The Portuguese went on to dismiss suggestions that tiredness was the reason for Tottenham's defeat, with the north London side having come into the game off the back of a Europa League clash with Inter on Thursday.
"I don’t think so, [it’s] nothing to do with tiredness. We looked very strong overall, our performance was excellent apart from a couple of mistakes," he added.
"Liverpool pressed us hard on that back pass that goes from Walker to Lloris and they deserve credit for that, for putting us under pressure really quickly. Moments like this can happen and you can’t be negative to the players who did ever so well to make a 12-game unbeaten run. Hopefully this setback can serve as an example to move forward."
After revealing that he expects both Emmanuel Adebayor and Clint Dempsey to return ahead of the second leg against the Italians, Villas-Boas lauded the recent contributions of Vertonghen.
"I think, like when we saw them against Arsenal, both central defenders [played well]," he continued. "Jan has been doing really well and he has adapted to this country very quickly. He’s a defender who scores goals and today he showed exactly that quality."