Chelsea lost Moises Caicedo to a red card in the first-half before Trevoh Chalobah had the hosts ahead. However, Mikel Merino found an equaliser just before the hour mark. But the Gunners couldn't find a second goal.
Asked if it is good sign that Arsenal were left disappointed not to get the three points, Arteta replied: "That's a good point. But that's the feeling that we have and that's the standards that we set for ourselves.
"Probably it's because of the spirit and the hunger and how much they want it. It's so incredible that we will overcome everything because already a lot of things happened. But that's it.
"What we have to do is prepare very well and Wednesday try to be better than Brentford."
Asked about fatigue, Arteta also insisted: "We played every two and a half days. Today we had one less day than Chelsea to prepare for that, and on top of that, we lost players. But it's the schedule.
"Now we're going to have to play on Wednesday for sure and every three days. It drives you on. It was a lot at stake. There were two very, very in-depth matches. But that's the beauty of it as well. Not many clubs had the opportunity this week to play the games that we have played. I'm extremely proud of the team."