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Tottenham midfielder Alli was determined to stay grounded following the draw, which left his side fourth in the Barclays Premier League table and six points behind leaders Arsenal.
He told Sky Sports 1: "As players we are not going to get too carried away. We are just going to take each game as it comes."
Alli was also disappointed his side did not take more from the game after dominating the first half.
Everton vs Tottenham player ratings
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"I definitely think we deserved more. That shows how well we are doing to come away to Everton and be disappointed with a point," said Alli.
Spurs defender Alderweireld echoed Alli's comments, saying: "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."
Everton manager Martinez said: "We have been a bit lightweight in the way we have defended our box and I thought today was an incredible change. The way we defended was a great platform for our performance.
"Spurs had a lot of the ball in the first half. The second half, the way we grew into it and the way that we could use the squad it was very pleasing.
"We could have taken one or two of the opportunities that we created in the second half but overall the performance was terrific."
PA
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