“It looks like it will go down to the wire at the end of the season for these Champions League spots,” Villas-Boas said.
“It’s part of the game – everything shifts very, very quickly in the Premier League but we have been in this position before and you have to deal with the pressure.”
Tottenham took the lead inside 34 seconds at White Hart Lane when Emmanuel Adebayor fired home Jan Vertonghen’s cross.
But Phil Jagielka headed home Leighton Baines’s corner to draw the Toffees level in the 15th minute, and Kevin Mirallas gave the visitors the lead seven minutes after half-time.
However, Spurs rescued what could prove to be a vital point when Gylfi Sigurdsson found the net after Adebayor’s shot had hit the post.
Everton boss Moyes, whose side are sixth and four points behind fifth-placed Arsenal felt the Merseysiders could have snatched a win in north London.
“One minute we were under pressure, the next we were breaking to score and it went that way through the second half,” said Moyes. “We were always a threat and scored a couple of good goals.
“Tottenham had a lot of chances themselves and we had to ride our luck at times without Marouane Fellaini and Steven Pienaar.”
Get enhanced odds of 18/1 on Andy Murray to win Wimbledon or 10/1 on Novak Djokovic when you open a Paddy Power account.