Spurs were leading thanks to Clint Dempsey’s opener until the 90th minute, when Steven Pienaar levelled for David Moyes’ men, before Nikica Jelavic grabbed a dramatic winner soon after to snatch victory.
“It’s really difficult to take,” Villas-Boas told BBC Sport. “We improved a lot from the first half to the second half. Maybe in the first half Everton could have gone 1-0 up.
“We came back strongly in the second half, played our best football and were a little bit more organised and I think we got the reward in going one up.
“But Everton did ever so well to bounce back. We tried to be on top of them to avoid those balls coming into the box.
“We had a chance to go two-up but in a couple of situations where we could have done better we didn’t and we ended up suffering.”
The Tottenham Hotspur manager was full of praise for his side’s “magnificent” effort following a hectic fixture schedule for the north Londoners.
“It’s been quite hectic for us in terms of fixtures so I congratulate the players because they’ve been absolutely magnificent in their effort,” he continued.
“They’ve come and played in a high-intensity game and almost came up with the result. We have to hold on to the positives and move on.”