Southampton boss Claude Puel was frustrated after his side failed to take their chances with the game scoreless.
He has been much-maligned this season after a relatively bright start to the campaign which included a scoring streak in the Premier League and a hat-trick against Ludogorets in the Champions League. "We'll know more in the next 48 hours".
After a boring first half, Sanchez produced a moment of magic to open the scoring when the Chilean wrong-footed two defenders in the box before calmly slotting home.
"We see ourselves as a top-10 club, and if we do fall short this season then we will put our hands up and acknowledge that, but I can assure you we will be far stronger next season".
"If we can not score with all these situations it is hard to win a game".
Wenger's opposite number Claude Puel lamented his side's inferior "clinical edge" to the Gunners after squandering the best chances in a tight first period. "I believe that I forget about that and focus on the game always". It's hard to accept.
Giroud, who came in for Danny Welbeck in the 80th minute, sealed the win for the Gunners just three minutes later with a header from inside the six-yard box.
"Stoke have only won one of their past nine games but are still in the running for a top-half finish".
Mesut Ozil also scored, finishing off a slick team move that showed the confidence Arsenal is starting to play with.
The Gunners' 12.5% win percentage (one win in eight) away at Stoke is their joint-second worst in the Premier League era (level with Sheffield Wednesday, one win in eight); they only have a worse win record at Manchester United (3 wins in 25, 12%). Despite this, Arsenal still remains in the fight for getting into the top 4, behind the fourth Man City by 3 points.
Chamberlain had been featuring as a make shift right wing-back in Wenger's new formation and is likely to be replaced by Hector Bellerin.
Ramsey has demons plaguing him over these past few years, particularly in Stoke City, but those aren't the demons I'm referring to that need to be buried.
Gabbiadini curled a free-kick wide before Cech was called into action again, touching a powerful Nathan Redmond effort over the crossbar.
Sanchez's goal was his 50th in the Premier League, his 21st of the season and his 15th away from home.