Boss Thomas Frank denied Brentford got revenge over West Brom after dumping them out of the Carabao Cup.
The teams were locked at 2-2 at the final whistle after the visitors twice cancelled out penalties from Hal Robson-Kanu.
The Baggies beat Brentford to promotion from the Sky Bet Championship by two points last season before the Bees lost in the play-off final but Frank dismissed any suggestion it was a revenge job.
Frank said: "That's the past, this is the future. We are pleased with the win in the cup.
"It was a good win in a tight game where it could have gone either way.
"We started the second half strongly until we made a mistake with the first penalty, we made a situation where we gave the referee a chance to make a decision. I was told it might have been outside the area.
"When you go to penalties anything can happen. I'm pleased all the practising paid off.
"I think it's a wonderful tournament. We are very pleased to have reached the fourth round, so can we win one more game to write history?
"Of course, we're interested in doing that."
Marcondes struck the post after 21 minutes and the Bees shaded the first half but they fell behind soon after the break.
Robson-Kanu was fouled by Dominic Thompson and he picked himself up to score his first penalty.
But Marcondes levelled two minutes later when his wonderful overhead kick from 10 yards, which deserved an audience rather than an empty Hawthorns, went in off the bar.
It forced a shoot-out and Diangana's penalty was saved by Raya allowing Christian Norgaard to score and send Brentford through.
Baggies boss Slaven Bilic said: "We're very disappointed with the result, we deserved to go through. It was a very good game between two rivals last year.
"I'm pleased with everything apart from the result. The way we played, especially in the second half, was very good.
"We didn't look like a team who was hanging on to the lead at 2-1. No hard feelings but it wasn't a penalty from Cedric, it was a great challenge with perfect timing.
"We wanted to go through and want to win every game. The game against Fulham or Sheffield Wednesday would have been at home so we wouldn't travel.
"It's not a blessing in disguise. Our priority is the Premier League but we wanted to go through."