The Baggies were denied a stonewall penalty early on in their 2-0 defeat at the Emirates.
Jay Rodriguez got up quickly after being brought down by Shkodran Mustafi to have an effort on goal.
But he saw his shot tipped onto the post by Petr Cech as Arsenal escaped.
Sanchez angered Pulis too and also went unpunished after the West Brom manager accused Arsenal’s star man of diving to win a free-kick.
The Gunners did not score from that incident but Pulis was unimpressed by the Chilean’s antics.
On the two key moments, Pulis told Sky Sports: ”I think everybody has seen what's happened today.
“I think if you want to make an example of something, Sanchez actually dives on the edge of the box for the first free-kick. And he should be booked for diving there, in my opinion.
"Then you see the tackle in the box on Jay, the referee's got a great view, it's a stonewall penalty.
“The great thing is everybody has seen it, so they make their decisions. I don't have to talk about it and I don't want to talk about it.
"It's not only a foul, the player could be sent off as well," added Pulis, though current rules mean the triple punishment of such an incident no longer exists. "So it could be a penalty and playing against 10 men.
"Jake [Livermore] should score the rebound and we should score other goals, we had opportunities.
“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 public out there, and everybody in the studio would have seen the referee's performance, so let them decide what they think. They won't get fined for that."
Arsenal won after Sanchez saw a first-half free-kick come back off the crossbar into the path of Alexandre Lacazette.
The Frenchman doubled the lead from the spot after referee Madley awarded Arsenal a penalty for a push on Aaron Ramsey by Allan Nyom.
