Emmanuel Adebayor took just 35 seconds to break the deadlock, the second quickest goal of the season, but Phil Jagielka and Kevin Mirallas looked to have earned the Toffees the points until Gylfi Sigurdsson struck with three minutes remaining.
"When you concede after 20 or 30 seconds it's all credit to the players for coming back," he said. "Tottenham had their tails up but thankfully we kept going and kept at it and played our way out of trouble and got ourselves a few chances.
"Tottenham had a lot of possession and we had to try and work to try and stop that. We didn't do it as well as we'd have liked but I always though we looked a threat and we could score and we did a couple of times."
Everton are now six points behind Tottenham in the race for fourth but have a game in hand, and Moyes added: "A draw isn't a bad result coming to Tottenham and I think you could see today both teams did try to win it.
"I don't know if a point does a great deal for us. If we'd lost the game we wouldn't have been out of it. If we'd won it we would have been right in it. I don't think we're too far away but the only thing is you just hope the games don't run out.
"Tottenham are one of the top teams who have been fighting for second, third, fourth all season and we've taken four points off Tottenham this year so it's not a bad return."
Moyes was pleased to see Mirallas on the scoresheet, with the Belgian in the middle of an excellent run of form after initially struggling to adapt to the Barclays Premier League.
"It was a terrific individual goal again," he said. "I thought he got better. I was disappointed with him in the first half as i thought we needed more from him going forward and also at times when we didn't have the ball I needed him to help us a bit more."
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- Kevin Mirallas