Hammers captain Jarrod Bowen swapped goals with Brentford striker Igor Thiago as the two teams finished extra-time at 2-2.
In the shootout, Dango Ouattara fluffed his Panenka attempt for Brentford, so seeing West Ham win on penalties, 5-3.
“What a long night!” Areola told whufc.com. “Three games in the FA Cup and three times playing until the last minute, but it was a great night, great atmosphere, and the fans were unbelievable tonight.
“We had a good moment, and I think it helped tonight as well.
“We (were) close to winning it (in normal and extra time), and we have details that obviously we can erase, but tonight we have to enjoy it.
“They're already playing my DJ set!
“All the things that I do outside football help me as well to stay focused and to just keep my head fresh and give everything.
“The team is the most important, but DJing keeps that positivity and helps me too.”