"I'm very proud because we played many young players but they showed they are good and can fight as well," said Wenger. "I decided to go for young players on penalties and they coped well with the pressure. "It's always good for them to know they can win when you think you're dead.
If you dig deep and are rewarded, that's an important lesson for a young player."
It was not all about relative unknowns, however. Mikel Arteta made his first start of the season following a thigh injury while Nicklas Bendtner returned for his first Arsenal appearance since August 2011.
Bendtner must have thought he had played his last game for the club but an aborted loan move to Crystal Palace earlier this month has given him another opportunity to display the talents he has not been shy to tell everyone about for years. The confident Dane later coolly converted his spot kick.
This was a fifth successive defeat against Arsenal for West Bromwich Albion and they will entertain a drastically different Wenger team when they meet again in the Premier League a week on Sunday. Steve Clarke's team were strangely subdued in the early stages, four days after administering the last rites for Paolo Di Canio's reign of terror at Sunderland.
The Arsenal goalkeeper denied Craig Dawson and Steven Reid in a cautious first half and the visitors were ahead in the 61st minute when Bendtner's clever pass released Eisfeld in the area, with the German midfielder finishing clinically.
Arsenal's lead lasted only 10 minutes. Graham Dorrans's corner was not cleared and Shane Long returned the ball back to find Saido Berahino, whose header finally beat Fabianski.
Berahino had scored a hat-trick in the previous round against Newport County and continues to enhance his reputation for both his club and England's Under-21s.
Markus Rosenberg squandered a glorious opportunity to prevent penalties four minutes from the end of extra time when he chipped the ball over Lukasz Fabianski but his effort was cleared off the line by Thomas Vermaelen.
So, to penalties. Luke Daniels saved Gnabry's spot kick but misses from Dawson and Morgan Amalfitano presented Monreal with the chance to finally end the game.
West Bromwich Albion (4-2-3-1): Daniels; Reid, Dawson, Lugano, Popov; Mulumbu, Dorrans; Sessegnon, Berahino, Sinclair; Long.
Subs: Olsson, Morrison, Rosenberg, Camp (g), Amalfitano, McAuley, Jones.
Booked: Lugano, Popov.
Goal: Berahino 71.
Arsenal (4-2-3-1) Fabianski; Jenkinson, Mertesacker, Vermaelen, Monreal; Hayden (Olsson 84) Arteta; Gnabry, Eisfeld (Akpom 82), Ryo; Bendtner.
Subs: Viviano (g), Flamini, Park, Bellerin, Iwobi.
Booked: Hayden, Monreal, Vermaelen, Hayden.
Referee: R Madley (W Yorks).
WBA Reid scored, 1-0.
Arsenal Bendtner scored, 1-1.
WBA Rosenborg scored, 2-1.
Arsenal Gnabry missed 2-1.
WBA Morrison scored 3-1.
Arsenal Olsson scored, 3-2.
WBA Dawson missed, 3-2.
Arsenal Akpom scored, 3-3.
WBA Amalfitano missed, 3-3.
Arsenal Monreal scored, 3-4.