The Hammers trailed to Leandro Trossard's late strike at the London Stadium, but appeared to have rescued a last-gasp draw when Wilson fired home after Arsenal keeper David Raya dropped the ball.
West Ham's celebrations were curtailed by a prolonged VAR intervention that ended with referee Chris Kavanagh changing his decision, ruling that Pablo had fouled Raya, after consulting the pitch-side monitor.
Nuno Espirito Santo's side remain in the relegation zone, one point behind fourth-bottom Tottenham, who have a game in hand against Leeds on Monday in the battle to avoid crashing into the Championship.
"A real blow. We thought we'd done so well to get back in it and had it taken away from us," Bowen said.
"When you look at the screen for five minutes, you'll find something, a lot of grappling and a lot of holding. Do I think it's the right decision? No.
"Where's the consistency? As a fan, you don't want to celebrate a goal and then wait eight minutes, and it's taken off you."
West Ham had appealed for fouls by Declan Rice and Trossard that could have led to a penalty in the Wilson incident.
And Bowen claimed officials are not consistent enough when dealing with potential fouls at set-pieces.
"Corners are physical. The Premier League is physical. That's why everyone loves it. You have to expect contact at corners," he said.
"If you give that, you have to give all the holding calls in the world, and that's not the way people want the game to go down.
"I don't want to sound bitter, but last week we had one with Tomas Soucek held at Brentford, and we didn't get a penalty.
"But then you can't give one like that today."
West Ham boss Nuno added: "The way the game finished, we're all upset, of course.
"I didn't pay attention to the replay just to not get more upset, but there's a referee, there's VAR, there's circumstances in the past that would be judged different. Let's not say much further than that.
"Due to the recent seasons, it's been happening, and even the referees don't know what is a foul, what isn't a foul. It creates a lot of doubt and speculation around it."