Arsene Wenger quiet on title chances
Saturday's top-flight results left the Gunners third in the table, level on points with second-placed Liverpool but considerably behind on goal difference, and four points adrift of leaders Chelsea, with all three having 10 more league matches to go.
Meanwhile, Manchester City, in fourth, are two points worse off than Arsenal and Liverpool and have two games in hand over the top-three sides.
Wenger described the loss at the Britannia Stadium, sealed by Jon Walters' 76th-minute penalty, as "a big worry" and "a massive setback".
But when asked how he assessed Arsenal's title chances overall from here, the Frenchman said: "I don't assess them at all, because I think what we have to focus on is our performance, and play well in our next game."
The rest of March looks absolutely crucial for Arsenal's title hopes, with their league fixtures seeing them take on fifth-placed Tottenham, Chelsea (both away) and then Manchester City at home.
With regard to Saturday's display, Wenger was in no doubt his side had not offered enough offensively, but said the penalty - awarded when Walters' flick struck Laurent Koscielny's arm - was a "nice gift" for Stoke from referee Mike Jones, and was also keen to praise the Gunners' defensive efforts.
"I think our defensive performance was outstanding," Wenger said.
"If you look well at the chances that Stoke had, I can see maybe one cross to (Stoke striker) Peter Crouch, and after that what did they create? Nothing at all.
"So you cannot say that our defenders didn't perform."
Neither were punished by Jones, but it seems the Adam incident may lead to retrospective action by the Football Association.
Potters boss Mark Hughes said it was the first he had heard about it when asked post-match about Adam's antics, adding that it would be "a shame if people highlight that as it wasn't that type of game".
He felt Stoke had been "excellent" in claiming a victory that moved them six points clear of the relegation zone.
Arsenal have won only once in six Premier League visits to the Britannia Stadium since Stoke's promotion to the top flight in 2008 - as well as losing an FA Cup tie there - and Hughes said: "I was made aware that in the last few years they have found it difficult here.
"I don't think they can have any complaints - we showed more intensity and more drive and determination in our play and that is what took the game away from them."
Stoke have also this term beaten Chelsea and Manchester United and drawn with Manchester City, all at home, and Hughes, appointed Potters boss last summer, added: "We have shown it at the Britannia against the top teams and we have to make sure we continue in the same vein against the teams around us.
"We haven't done that on too many occasions but have opportunities now to put more points on the board."
Asked why he thought his side were producing positive results against major clubs but often struggling to do so when playing less high-profile outfits, Hughes added: "I don't know - I've been trying to work that out myself!
"When we play top sides there is intensity, a determination and drive from us.
"More often than not the top teams dominate possession so we have to have a different game plan.
"We have struggled against lesser teams because when the onus is on us to take games to the opposition sometimes we are not as accomplished, and we need to get better at that as we need to find a way ourselves in the key games coming up."