Wenger's first XI for the contest featured nine adjustments from Sunday's Barclays Premier League win over Stoke and several players inexperienced at senior level.
The contest finished 1-1 after 120 minutes, with Albion substitute Morgan Amalfitano having hit the bar in a strong conclusion to extra time for the hosts.
The Baggies then initially had the advantage on penalties after Serge Gnabry's effort was saved, but fellow Arsenal teenagers Kris Olsson and Chuba Akpom subsequently netted theirs and Craig Dawson and Amalfitano missed for West Brom, allowing Nacho Monreal to seal a 4-3 shoot-out triumph for the visitors.
Wenger - whose team host Chelsea in round four - said: "I am proud. We played with many young players and they showed they are not only good footballers but that they can fight as well.
"I decided to go for young players with the penalties and they coped well with the pressure.
"Of course, penalties are a bit of a lottery, but overall I think the most important thing is that we played well in the game and that the young players came out and showed that they can play the way we want to.
"It is always good to know that you can win even when you thought you were dead and tired.
"If you dig deep and in the end you are rewarded, that is a very important lesson for a young player.
"We kept going forward and trying to win the game until the end and that is very positive."
On Bendtner, who provided the through ball for Eisfeld's goal, Wenger said: "I thought overall, he had a good game.
"For a guy who has not played for such a long time, and on his own up front, he did very well."
In extra time, Bendtner was through on goal but had the ball taken away from him by a superb Dawson challenge.
Asked about that incident, Wenger said: "What happened to him is what happens to many strikers when they have too much time to score - they wait and wait, and wait for too long. But overall, I thought his game was positive.
"I believe for Nicklas, the most important thing for him is to stay fit. As for the rest, he has the talent - you know that."