The young Arsenal side won the shootout 4-3 after 20-year-old Thomas Eisfield had his second-half opener cancelled out by West Brom's Saido Berahino to see the match finish 1-1 after 120 minutes.
Wenger was delighted with how his side played, with youngsters such as Eisfield, Serge Gnabry (18 years old), Isaac Hayden (18) and Chuba Akpom (17) looking capable of playing Arsenal's style.
"I am (proud) because we played with many young players and they have shown that not only are they good football players but they can fight as well," Wenger said after Wednesday's tie.
"The penalties were a bit of a lottery but overall I think the most important thing for me is we played well during the game and the young players came out and showed they can play in the style we want to play."
Danish striker Nicklas Bendtner made his return to Arsenal's line-up after loan spells at Sunderland and Juventus, making only his second competitive appearance for the London club since the start of the 2011/12 campaign.
Wenger believes Bendtner can contribute to Arsenal's season, with the 25-year-old forward being the only experienced alternative to preferred lead striker Olivier Giroud.
"One thing you don't question too much with (Bendtner) is his confidence," Wenger said.
"I believe for the most important thing is to stay fit physically and after that he has the talent.
"In England, you know him well and for him it's important that he's consistently present and he works hard physically because he has the top qualities."
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