The Gunners couldn't find a second goal despite Chelsea losing Moises Caicedo to a red card.
"It was an intense game, a good battle," Odegaard said afterwards. "Both teams started really aggressively, started strong, there were a lot of duels. Obviously, with the red card, we feel like we should have won the game and done a little bit better in certain areas of the game. In the end, it was a tough battle and a point, so we'll have to take that and move on, and make sure we win the next one.
"It's been a massive week for us. Some big games, some big results. Today was another big test for us. We wanted to come here and finish off the week with a win, but as I said, it was a tough battle. They were fighting really hard for it and we didn't do enough to win the game, so we move on and now we just have to make sure we win the next one."
Odegaard was a second-half substitute on the night as he continues to work his way back from knee injury.
"It was amazing to be back out there," he said. "I missed it a lot. It's been a weird season for me. I've been out for a while now, but I was really focused on the result. So yes, it's been a weird season for me, but I'm back out there and feeling good."