A double from Alexandre Lacazette sealed the win for the Gunners at the Emirates Stadium and moved them back to within six points of Premier League leaders Manchester City.
There was a controversial moment in only the eighth minute when Rodriguez, having been brought down by Shkodran Mustafi in the Arsenal penalty area, got back to his feet and saw a shot tipped onto the post by Petr Cech, before Jake Livermore missed the rebound.
Pulis was far from pleased to see referee Bobby Madley refuse to award a spot-kick and felt Rodriguez was punished for being "honest", given that Sanchez had earlier won a free-kick in a dangerous position after going to ground following minimal contact from Craig Dawson.
"Everybody's seen what happened," the West Brom boss told Sky Sports . "If you want to make an example of something, with Sanchez, the first free-kick he gives on the edge of the box, he should be booked for diving.
"Then you see the tackle in the box on Jay, the referee has got a great view and it's a stonewall penalty.
"It's not only a foul, the player could be sent off as well. So it could be a penalty and them down to 10 men.
"Jake should score the rebound and we should score other goals, but the disappointing thing is Sanchez falls for the first free-kick and he should be booked. That's cheating.
"Jay is very, very honest and doesn't get any reward for being honest. We haven't had a penalty at this football club for over and a year and none of my players are told to roll around.
"The great thing is everyone has seen it and I don't have to talk about it, and I don't want to talk about it. I thought we played really well, we missed a lot of chances in the first half. We're disappointed."
Rodriguez insisted there was definite contact from Mustafi and defended his refusal not to make more of the incident at the time.
"I felt contact and obviously went down. It wasn't given, I got back up because I wasn't hurt and saw a chance to score and Cech made a good save," he said.
"For me, it was a penalty. It's disappointing.
"I'm not going to be rolling round and trying to buy free-kicks if it's not a free-kick. There was a decision there to be made and it's one of those things.
"If you get the goal, you're 1-0 up and it changes the game. We've got to move on and I thought we did well in the end."
Lacazette's second goal came from the penalty spot after Aaron Ramsey was bundled over by Allan Nyom in the same area, but the Wales midfielder felt the referee got his decisions right.
"I was up the other end of the pitch. I didn't quite see what happened but I'm sure there was contact, but the referee played advantage," Ramsey said of the West Brom appeals.
He added on Nyom's foul: "I thought I took it round him and he pushed me out the way. I think it was a penalty."