In a first XI for the Albion match featuring nine changes from the Barclays Premier League win over Stoke on Sunday, there were maiden Gunners starts for Thomas Eisfeld and Ryo Miyaichi, both 20, and a debut for Isaac Hayden, while fellow 18-year-old Serge Gnabry kept his place.
And after midfielder Eisfeld had slotted in the opening goal in the 61st minute and Saido Berahino headed an equaliser 10 minutes later, Wenger brought three more teenagers off the bench in Chuba Akpom, Kris Olsson and Hector Bellerin, the latter pair making their senior bows.
The score was still 1-1 after extra time - Baggies substitute Morgan Amalfitano hit the bar during the additional period - and penalties were required.
Gnabry saw his effort saved but Akpom and Olsson both converted theirs in a 4-3 triumph for the away side, sealed by Nacho Monreal's successful effort following Albion misses from Craig Dawson and Amalfitano.
Wenger spoke after the third-round tie of his pride at the youngsters' battling sprit and ability to cope under pressure, but asked about blooding such players again in round four, he said: "Honestly, I don't know yet.
"It depends on the injuries. I had no choice but to rotate because many senior players are out."
Going into Wednesday's match Wenger had Santi Cazorla (ankle), Theo Walcott (stomach), Tomas Rosicky (thigh), Yaya Sanogo (back), Lukas Podolski (hamstring), Alex Oxlade-Chamberlain and Abou Diaby (both knee) all unavailable.
The manager added: "In our job we have all started when another player was injured.
"You have opportunities that you have to grab with young players. When there are players who are injured, they can show they have the quality."
West Brom's starting line-up showed eight adjustments from their league win over Sunderland, and while youth had been injected in the shape of 20-year-old striker - and second-round hat-trick hero - Berahino, someone else coming in was veteran Steven Reid, who captained the side on what was first appearance of the season.
The 32-year-old defender has been recovering from a calf problem and reflecting upon his comeback match, in which he almost scored with a first-half free-kick and lasted the entire duration, Reid told wba.co.uk: "It was my first game back and I'm pretty tired.
"I was going to say it's my first 90 minutes but it's my first 120 minutes of the season.
"I came through it and though I was a bit tired towards the end of the 90 I found a little bit extra for extra time.
"I'm happy to have come through the game.
"Hopefully I can stay fit and start pushing to get into the Premier League first team.
"(Fellow full-back) Billy Jones has been superb this season.
"I need to be ready when my chance comes."