Arsenal lost 1-0 at Villa Park on Saturday after John McGinn scored the only goal of the after just seven minutes.
Arsenal had a good shout for a penalty waved away during their loss at Villa after Douglas Luiz appeared to catch Gabriel Jesus in the area.
They also had a late goal disallowed after Kai Havertz was judged to have handled the ball before bundling it home.
But Odegaard said: “We have to focus on ourselves. We can’t think too much about the other stuff.
“We have to look at ourselves, look at what we could have done better and I think especially in front of the goal, we should have done a bit better and in some periods of the game we should have controlled it a bit more.
“As I said we did enough to get a result but we have to be more ruthless in front of goal.
“When you come to a place like this it is always tough. So you have to be ruthless in front of goal – myself included, I missed a few big ones, so that’s annoying but the only thing we can do is work hard to improve and bounce back in the next one-on-one.”
Arsenal have made a good start to the season and they are only a point off League leaders Liverpool.
Arteta’s side have also progressed to the last 16 of the Champions League as winners of Group B and their match next week at PSV Eindhoven is a dead rubber.
“I think we’re up there,” said Odegaard, when asked to assess Arsenal’s season so far.
“We were top of the League before this round and now we’re second. So we definitely up there and there is still some room for improvements in the team and what we're doing but I think it's good progress.
“I think we’re getting better and better and it is going to be exciting.
“All the games are so hard and you see now at the top there are more and more teams fighting and competing there.
“So of course it’s the toughest league in the world but that’s what we’re playing for and we enjoy that competition. So we have to keep going, learn from the mistakes and come back better.”