Alexis Sanchez's free-kick deflected in via James McClean to put the Gunners on the brink of victory at The Hawthorns as Wenger ticked onto 811 Premier League games managed - a new record.
However, Mike Dean awarded the Baggies a penalty late in the game after Kieran Gibbs' cross hit Calum Chambers' arm from point-blank range.
Arsenal fumed at Dean after the match with Petr Cech earning a yellow card, and Wenger then launched a scathing attack on the standard of officiating.
"What can we do? We can talk and talk but it doesn't change," Wenger told Sky Sports.
"The Premier League doesn't face the problem, not with the schedule and not with the referees. Years ago, the referees turned professional but the level doesn't go up.
"In my opinion, yes, it is 100 per cent wrong. It is difficult to accept. It is not the first time, but it is best not to talk about it. We just have to deal with it."
Wenger had no doubt that VAR would have spared his team, adding: "I think it will make a difference. We want to be the best league in the world so it is time to use it. Other leagues do."
Opposite number Alan Pardew freely admitted that his side had enjoyed a significant rub of the green with the decision.
He told Sky Sports: "When you keep talking about doing the right things and application and earning luck, and it doesn't happen, it's hard, but we got it today, at last.
"The decision's a tough one on Arsenal. I've seen it and, wow, he could've not given it. But we deserved the break."