Arsenal couldn't hold on after Odegaard's opener
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"It's a hard one to take. I think in general we were not at the level we needed to be at today," Odegaard told Sky Sports after the defeat.
"We had some good moments but we have to do much better. We should have been better.
"It's hard to say. That's just how it is sometimes. It's hard to say exactly what happened. We have to do better when we have that lead. We stopped playing and gave them the game they wanted to play."
When asked whether he felt a mindset problem was to blame for the Gunners surrendering their lead, the 22-year-old said "I think it is".
"When you're leading 1-0 you get afraid to lose the win and in my opinion that's what we did wrong today," he said.
"You go for the second goal and that was the intention but we didn't manage to do that on the pitch."
It was the second successive game in which Mikel Arteta's team have thrown away a lead, after they were pegged back at Old Trafford following Emile Smith Rowe's early opener.
Odegaard scored in that game too, bringing Arsenal back level in the second half before Cristiano Ronaldo's second of the evening gave Manchester United the points.
Gray gave Everton victory in stoppage time
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Gray's stoppage-time goal brought Everton victory after a run of just two points from eight games, easing some of the pressure on manager Rafa Benitez.
"It was a crazy moment. My best moment here so far," the former Bayer Leverkusen winger said.
"It was important for us to get that win. As a group we have gone through this bad patch but we have stuck together. With the fans like that, behind us for the whole game, it's more than deserved."
Arsenal will need to turn things around quickly, with back-to-back home league games on the horizon against Southampton and West Ham, while Everton's next game sees them up against out-of-form Crystal Palace at Selhurst Park.