Spurs leapt to an early lead when Emmanuel Adebayor scored inside the first minute but found themselves behind after Phil Jagielka (15th minute) and Kevin Mirallas (53rd) had the Toffees ahead.
But Gylfi Sigurdsson came up with an 87th minute equaliser which allowed Spurs to stay fourth on the table, two points clear of fifth-placed Arsenal, and although it wasn’t the exact result the club wanted, Villas-Boas was content.
"I don't think we relaxed," he said.
"You give Everton a small amount of space and they punish you.
"It was an entertaining game of football.
"I think it was a good performance by the team, individually and collectively, although it was not the result that we wanted."