Villa shook off a lacklustre first-half display as goals after the interval from Fabian Delph and Scott Sinclair saw off their near neighbours at Villa Park.
Sherwood and his players must now return to the reality of a battle against relegation in the Premier League before their trip to Wembley next month - something the former Tottenham boss believes can boost the whole club.
"It's huge, a massive for the club and we're delighted," he told BBC Sport.
"I spoke to the boys in there and I'd like to dedicate it to the fans. They've stuck with us.
"It's great as a day out at Wembley is a great day out for everyone and the fans especially.
"I thought it was boring in the first half and I had a few words during the break and told them to step it up and it worked."
Sherwood's decision to highlight the Villa supporters was a touch surprising as fans entering the field of play during the closing stages of the match preceded a full-time pitch invasion - events that could prompt punishments from the Football Association.
Villa captain Delph said the scenes at full-time were "very, very scary", but his manager disagreed.
"You want to celebrate with the whole crowd," Sherwood said. "I don't think it's scary, it probably is for a West Brom player.
"Emotions are running very high. It's been a huge week for the football club."
Both teams finished with 10 men as West Brom's Claudio Yacob and Villa substitute Jack Grealish were given second yellow cards - decisions that Sherwood felt were out of keeping with the contest as a whole.
"I didn't see a bad tackle in the whole game," he added.
"It's a shame for Jack Grealish who has his head down in there, but there's plenty more opportunities for him."
