Clint Dempsey's deflected shot put Tottenham ahead and the score stayed at 1-0 until 14 minutes from the end until Steven Pienaar and Nikica Jelavic scored within 88 seconds of each other in the 90th minute and added time respectively to secure a deserved victory for the home side.
Spurs have developed a poor record for conceding late goals - 10 in the last 15 minutes - and that cost them again.
"It was a disappointing result bearing in mind we were leading taking the game into the last minute," Villas-Boas said.
"It has been quite an adventure in the Premier League this season; if we count the number of results that have been going for us before the last minutes we would be first.
"There are so many different reasons. It is not really easy to explain because a couple of them come from different situations.
"It is something we are aware of, which is why we speak about it openly, and it is something we have to improve, seeing off games.
"It is not a mental thing, it is the nature of the game because it was our best period for quite some time in the second half.
"You kind of knew as soon as the kick-off went for the 1-1 they (Everton) would go and have a go and they certainly did.
"It is a difficult blow to take."