Gylfi Sigurdsson earned Spurs a share of the spoils after Phil Jagielka and Mirallas - the latter with a fine solo effort - had cancelled out Emmanuel Adebayor's first-minute goal at White Hart Lane. The Merseysiders were missing key men Marouane Fellaini and Steven Pienaar due to suspension, and Moyes hailed Mirallas for stepping up in their place.
"Mirallas was our individual today and did what Gareth Bale may usually do," the Toffees boss told reporters. "I thought Mirallas got better in the second half, and his goal showed why you stick with strikers. Even after his goal we had a couple of chances to make it 3-2.
"It was going to be hard anyway but today we went to try and win it and we made a change, got a goal and we had to defend a lot after that. So we’ve done everything we possibly can to get a result.
"We’re playing a good team. We’ve taken four points off Spurs this year. We’re trying to hang in there. Does [the result] help us? Probably not.
"But I said before today that if we had lost today we would still be right in the mix. What does a draw do? It shows we played well enough to get a point.
"Tottenham played well but in truth we should have nicked the game at the end. It was a really good game, with both sides trying to win."
Everton was not the only side to be missing important players, however, with the likes of Bale, Aaron Lennon and Jermain Defoe all missing from Andre Villas-Boas' matchday squad. Moyes, though, said that Spurs players stepped up to the mark and that Everton felt the absence of its stars more acutely.
"I think we missed our players more – Tottenham’s players played really well today," Moyes said. "I think with our squad to come away from Tottenham with a draw is fantastic. We were juggling with our players. We shouldn’t be disappointed with a draw.
"We knew we had to win to stay in amongst the race for the Champions League spots. We’ve got tough games but Tottenham are as good as anybody so a draw here is encouraging.
"I’m disappointed not to take three points but not outrageously disappointed."