Emmanuel Adebayor had given Spurs the lead in the first minute before the Toffees turned the game on its head with goals from Phil Jagielka and Kevin Mirallas.
But Sigurdsson snatched an equaliser with three minutes remaining to claim a point that could prove vital in the hunt for a Champions League place.
"It was very important for us," he told ESPN. "After going 2-1 down it was important we didn't lose the game.
"We could have done with three points here today [Sunday] but at the end we were happy to get the point.
"In the second half after their goal they dropped down and we had a lot of chances to cross the ball in and a couple of half chances and we're happy with the point.
"We started the game really well but they're a tough team to play against. They made it difficult for us in the first half but we got there in the end.
"It was important not to lose the game because they're obviously up there with us. Many teams are still up there and it was good to get the second goal."
Everton boss David Moyes was happy with the way his team responded after going behind so early.
"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.
"But that's why you have those players. Those players are the ones who can waltz past a couple of people and get you a goal."
Jagielka is also pleased Mirallas has found his feet, adding: "We'd have liked him to settle in as soon as he got here and score goals like that from the beginning.
"It's hard to judge. It's his first season in English football and it will be different from what he's used to but he's definitely putting in a lot better performances and hopefully it can continue."