Spurs struck the post twice as they dominated the opening 45 minutes but went into the dressing room with the score levelled at 1-1 thanks to Dele Alli's fine volley after Aaron Lennon's opener for the Toffees.
The Belgian defender told Sky Sports.: "The first half was one of the best halves of the season for us. I think we lost two points today.
"We are very solid at the back and at the front we have a lot of quality too. We have to keep going and working hard."
The draw left Spurs sitting fourth on the Premier League table, six points behind leaders Arsenal.