The draw left both Newcastle and Everton on 30 points, six points clear of the relegation zone.
Newcastle manager Steve Bruce was delighted by his team's endeavor after the Magpies scored twice in stoppage time to salvage a point.
He said: "We keep showing determination. We were a tired team tonight but we found a bit of energy from somewhere.
"When we scored Mike Dean said there are 40 seconds left - and you're thinking 'can we score in 40 seconds?' We rode our luck certainly but they never gave up.
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"There is a good spirit and attitude in this team - we looked tired but we played people out of position. We didn't have much coming off the bench in terms of forward players but the attitude was fantastic.
"It's a wacky game that's for sure - but it's great. It just shows you shouldn't leave a game early."
Everton manager Carlo Ancelotti was pleased with his side's performance despite throwing away a two-goal lead.
Jordan Pickford was trolled after Newcastle secured a point at Goodison Park (Image: GETTY)
He said: "There are things in football you cannot control. We conceded without any reason but the performance was good.
"We played a fantastic game and we were unlucky but nothing changes - our Premier League continues, we have to stay focused.
"We were two-nil up, had opportunities to score and we played attacking football. I'm really pleased with the performance. These results are not frequent but they can happen.
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"We have to stay on the game for 90 minutes but I'm not saying anything to my players. They played well and it can happen. It's just unlucky for this game."