Leading 1-0 at Goodison Park through Clint Dempsey's goal 14 minutes from time, Spurs were primed to take all three points, win their fourth consecutive game and keep the heat on third-placed Chelsea in the Premier League.
However, Steven Piennar scored against his old club to equalise in the 90th minute before Nikica Jelavic grabbed the winner in added time, vaulting Everton into fourth and leaving Villas-Boas distraught.
Spurs have kept a clean sheet only once away from home this season, a 3-0 win at Fulham earlier this month, and have conceded 10 of their 25 goals in the last 10 minutes of games.
"It's difficult to take," the Spurs coach told the team's official website.
"The last minutes were our best with Clint's goal ..., we kept the ball and played well, but then the game changed completely against the run of play."
The visitors almost went 2-0 ahead but Gylfi Sigurdsson's shot hit the crossbar.
"To be fair, Everton had a first half where they could have scored, that's the reality.
"But we managed to hold on to that 0-0, then had a brilliant second half and to see it escape from us in the last minutes is difficult to take."
Everton manager David Moyes said his team had been on the wrong end of some late dramas and it was about time fortune favoured the Blues.
"After the few finishes like that where we have lost points we were due one," he said. "If Everton hadn't won we would be sitting here asking how we hadn't. We played terrifically well and the attacking play we had was fantastic."
Everton, who have yet to lose at home this season, looked vulnerable after Dempsey's goal as Moyes changed things around in the hope of grabbing an equaliser.
"I actually think our poorest passage of play was in that last 10 minutes," said Moyes. "We were trying to move players around, it was scrappy and we had tried everything to get ourselves an opening.
"But we kept at it and we got it in the end." (Editing by Patrick Johnston)