The Gunners surrendered a lead to lose 2-1 to the Toffees on Monday and the midfielder feels it is down to a mental issue.
Martin Odegaard says a mental problem cost Arsenal as they lost 2-1 to Everton on Monday.
The Norwegian midfielder scored just before half-time to put the Gunners 1-0 up at Goodison Park, but Richarlison and Demarai Gray fired in the second period to secure a first Premier League win since September.
Arsenal, meanwhile, have now lost two matches in a row in the English top-flight and Odegaard feels their mentality cost them in the latest upset.
"I think it is [a mindset problem]. When you're leading 1-0 you get afraid to lose the win and in my opinion that's what we did wrong today," Odegaard told Sky Sports after the match.
"You go for the second goal and that was the intention, but we didn't manage to do that on the pitch."
He added: "It's a hard one to take. I think in general we were not at the level we needed to be at today.
"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."
Arsenal manager Mikel Arteta was disappointed in his side's performance against the Toffees, admitting their use of the ball was not good enough.
He told Sky Sports: "In the first half we were very inconsistent with the ball. I didn't like it. No penetration. One of the few times we did it we scored. Second half we tried to do more of those things, created four big chances but conceded a very sloppy goal when you need to manage the game.
"We couldn't take the ball into the final third. They're not going to give you time, at Goodison you know what to expect. I think the team tried to go, we kept pressing high. We lost a few important duels that put us some pressure."
Arteta's team are currently seventh in the Premier League and 12 points behind leaders Manchester City.
They host Southampton in their next match on Saturday, which will be followed by a home match against West Ham four days later.