The borough of Haringey, in which White Hart Lane is situated, witnessed the start of the trouble on Saturday night and this weekend's game could join tomorrow's England friendly in being called off if police resources are needed elsewhere.
The players are continuing to prepare for the match as normal, and defender Sylvain Distin said: "We can't do much about it so we'll just get ready and try to do everything as if the game was on."
The Frenchman has shocked by the scenes, which last night spread to Liverpool, and he added: "It's madness. I've watched it on TV and it looks like a war zone.
"It seems unreal. Football right now is not the most important thing. I know the fans expect the season to start but when you see what's happened, it's more important than whether the game's going to be on or not."
Everton have been one of the quietest clubs in the summer transfer window, with only young defender Eric Dier arriving on loan from Sporting Lisbon while Iain Turner and James Vaughan have left.
Distin highlighted the fact the Toffees have been able to hang on to star names like Phil Jagielka, Leighton Baines, Mikel Arteta and Tim Cahill, at least for now, as a positive indicator for the new season.
He said: "I think we've got enough quality and the most important thing is to keep our best players, which so far is the case. That's a positive and a strong sign.
"Any team and any player would like to improve their squad, so everybody wants to see new players coming.
"But the fact we don't have too many players every season is a positive as well because it means you play with the same guys so you get to know each other a bit more and create a good team spirit."
Defender Jagielka has been consistently linked with a move to Arsenal this summer, but Distin insisted that has not had a destabilising influence on the squad.
He said: "Why should it affect us? Right now he's here, there's no sign that he's going. The club refused the offer from Arsenal. There's no reason to be worried."
A section of Everton fans have become increasingly disillusioned by a perceived lack of investment in the playing staff, prompting chief executive Robert Elstone to write a blog on the club's website last month defending their approach.
Distin played down the issue, saying: "I don't think there's any club that I've played at where the fans have been happy with what happens during the transfer window.
"They have to remember that we've kept our best players so far. We have to give the club time and maybe things will happen soon."
Asked if it will have an impact on the team, he said: "It affects us if the fans are not behind us. If you play a home game and feel like you are away because there is no atmosphere, or you can feel the tension or the disappointment from the fans. But I'm sure the fans love the club and the players enough to support us."
Supporters' discontent has been heightened over the past couple of seasons by poor starts, with Everton failing to win a Premier League game until October in the last campaign.
They recovered to finish seventh, and Distin sees no reason why they cannot aim even higher this season.
"It's where you finish that matters, not how you start," he said. "There are teams that have started really well and ended up being relegated, so I don't think it has any importance.
"I think we've been quite close to the top four so I don't think it means the club is going the wrong way. It will be difficult to get into Europe but difficult is not impossible."
Distin also does not believe too much should be read into Everton's pre-season results, which have included defeats by Philadelphia Union, Werder Bremen and Villarreal.
He added: "I don't think in pre-season the results are the most important thing. It's more about the fitness and not getting any injuries. We feel good."