The Gunners won the match 2-0 thanks to two goals from Alexandre Lacazette, the second of which was from the penalty spot after Allan Nyom bundled over Aaron Ramsey.
Given his side had a clear penalty turned down in the first period when Jay Rodriguez was taken out by Shkodran Mustafi, Pulis was not happy when speaking to Sky Sports and singled out Sanchez when discussing simulation:
"The disappointing thing tonight is Sanchez dives for the first free-kick, not the one they score off, and he should be booked. That's cheating. Jay is honest, and doesn't get his reward for being honest. We haven't had a penalty at this football club for over a year. And none of my players are told to roll around."
The match had plenty of controversy, with the most striking incident being the decision not to award the Baggies a penalty.
Sports writer Chris Smith believes that if Rodriguez had made more of the challenge instead of getting up and trying to score—his subsequent strike was tipped on to the post by Gunners goalkeeper Petr Cech—the penalty would have been awarded:
Chris Smith @cdsmith789
Rodriguez pushes the referee towards not giving that pen. Gets up as if he wasn't caught. Pretty daft play to be honest.2017-9-25 19:11:02
Arsenal manager Arsene Wenger had a different view on the penalty to Pulis, suggesting referee Bobby Madley opted to play a bold advantage.
"The referee left the advantage and they nearly scored from that and they hit the post," the Gunners boss said, per Miguel Delaney of The Independent. "The decision is defendable on both sides."
The incident involving Sanchez didn't lead to a goal for the Gunners and wasn't immediately obvious, as noted by sports writer Jonny Singer:
Jonny Singer @Jonny_Singer
Anyone got a video of the Sanchez 'dive' pulis was speaking about2017-9-25 21:55:01
Sanchez went down early in the game after a run towards the penalty area. He does have some history in terms of simulation, having been booked for diving in the Premier League last season during the 2-0 win against Hull City.
Still, it's difficult to say with certainty whether a player is "cheating." In the case of someone like Sanchez, who moves with such pace and agility, any type of touch is enough to send him to the floor, especially from some of the physical defenders West Brom have on their books.
The Baggies will feel hard done by after this defeat, though Pulis will know—regardless of the decisions made by the referee—his team spurned enough openings that would have helped them take a positive result from this fixture.