The Gunners dominated possession but, just like last week's match against Sunderland, could not make the most of it.
"It [two points from the first two games] is not good enough. We wanted the three points, but it is a hard place to come and try to get the points," Arteta told Sky Sports 1.
"We had some really good chances but at the moment we are not taking them, the same thing happened last week.
"We are making them and conceding few chances to the opposition but we lost two points again today."
Defensively, however, Arsenal looked solid and dealt with the physical threat of the hosts.
Arteta was keen to praise the backline and talk up the ability of the new signings Olivier Giroud and Lukas Podolski.
"You know if you concede fouls and throw-ins they can put you in trouble because they get the ball in the box and are really organised at set pieces," he said.
"We didn't concede many chances and were well organised.
"We need three, four, five games together and then we will see (how good they are).
"They have the quality."
Arsene Wenger was pleased with how his side defended and admitted he was keen to bring in more players before Friday's transfer deadline.
"(Defensively) overall we did very well, our defenders, our midfielders,(Abou) Diaby had a good protection role in midfield. Our back four did well, our goalkeeper did well," the Arsenal manager said on Sky Sports News. "They (Stoke) are a handful for anyone that comes here.
"I'm pleased with what I have, but yes I anticipate that we will do something still, we are still on the market. Defensive midfielder, it depends on the quality of the players available."
His counterpart Tony Pulis was equally satisfied with a point and like Wenger expects new arrivals at his club.
"It was a good result, there are things we are not happy with and can do better," he said.
"We were playing a team on a different level.
"We have a busy week ahead so we can freshen it up a bit. We have played two difficult games we are still unbeaten."
Regarding reinforcements, Stoke agreed personal terms with Rangers midfielder Maurice Edu yesterday and are also looking to bring in Tottenham midfielder Tom Huddlestone.
"We have taken the lad Edu, well, we are hoping to do a deal," Pulis added.
"As a football club we have to go a bit careful, the chairman has been wonderful. We have to wheel and deal a bit more this year then before.
"I'm hoping, praying one or two things drop for us, we need to freshen it up.
"That [Huddlestone] was going on Friday, we will hopefully revisit that on Monday."
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