Everton manager David Moyes conceded they must win all of their remaining games if they are to have any hope of a top-four finish.
Despite plenty of endeavour, Arsene Wenger's hosts were unable to break down a determined Everton side, who utilised all their physical qualities.
A satisfied Moyes said: "It was a really good game. It was end to end and we played some really good stuff. I'm not too despondent with a point, even though we wanted to win. We got about the game, went after it. We were trying to make a real game of it.''
Arsenal's best chances fell to Olivier Giroud, but the France striker failed to test Tim Howard, while Sylvain Distin and Seamus Coleman combined to clear away a real moment of danger when Alex Oxlade-Chamberlain centred the ball with Giroud ready to pounce.
"We got a little bit fortunate,'' Moyes added on Sky Sports 2. "A couple of bits of defending were fantastic to ensure we didn't concede a goal.''
Moyes said that while the point keeps alive their Champions League hopes, he feels they must not drop any more over their final five games if they are to close the two-point gap on Chelsea in fourth.
"I am pleased with the performance, and with the result. You are never disappointed taking a point at the Emirates, you can't be with the quality they have here. We went to try and win it. We knew if we got three points here we would have a real chance (of the top four), but a point keeps us ticking along.
"I think that result suits Spurs more than anybody... but I don't think we are out of place where we are. It is hard for us compared to clubs like Arsenal, but we go out on the pitch and do everything we can to beat them, make sure they don't beat us. Everton, as a team, played really well tonight.
"I would take it (the Europa League), but I am going to try and get the Champions League - if we are still getting that mention in mid-April, then it is not bad for Everton.''
Arsenal manager Arsene Wenger maintains his side still have what it takes to finish in the top four.
"We should have won the game, but it still keeps us in a strong position in the race for the top four,'' said the Arsenal manager. "We had the chances to score, and that's my regret. Maybe we used power instead of technique too much in our finishing.
"My belief was always strong and still is. I am confident we will do it. The best way is to put the same effort into the next game.
There were plenty of hefty challenges from the visitors, notably from Darron Gibson in the first half on Theo Walcott - with the midfielder fortunate not to have been shown two yellow cards in succession by referee Neil Swarbrick for body-checking the England winger.
Wenger was not impressed. He said: "I felt that in the first half the referee didn't deal at all well with the intimidating physical challenges, but that we responded well to the physicality. It was detrimental to the fluency of our game, but we kept going, had good concentration.
"But that is part of the game. We had to deal with that. You have to respect the effort Everton put in. They decided to make it very physical for us to disturb our game and sometimes went a little bit over the edge, but the referee had to make the right decision.
"I don't blame Everton for that. 'Protecting' is a big word, but they (referees) have to make the right decisions.''
Wenger challenged his men to bounce back with a win at Fulham on Saturday.
"We are on a very strong run with a fantastic run so we do not want to complain too much about what didn't go for us,'' he said. "Let's look at ourselves, come back in the next game and win it.''
Gunners midfielder Jack Wilshere started his second match in four days since returning from an ankle injury, and television pictures showed him involved in a half-time spat with Everton's Kevin Mirallas.
Wenger, though, said: "I don't know about it, but if it was (on television), then very soon everybody will know about it - and I will know about it as well. It was all right in the dressing room.''
Everton boss David Moyes defended his side's approach. He said: "Do you mean when we were a little bit rough with the tackling? Up north we do that quite often, that's actually allowed in football. We weren't going to come here and let Arsenal stroke the ball around and make 600 tackles.''