Villa picked up their first league win under their new manager by beating Albion in the Premier League on Tuesday, lifting them three points outside of the relegation zone.
A stoppage-time winner from Christian Benteke's penalty saw Sherwood take to the pitch at the final whistle and put his fingers to his neck, indicating Villa's pulse was still beating in the fight for survival.
And the former Spurs boss then quickly turned his attentions to the cup.
"[There is] no chance [of a rest]," he said after the victory. "It's the quarter-final of the FA Cup.
"This win gives the club a huge lift. Now we want to get to Wembley. We want to be in the semi-final.
"The Cup is now the most important one as it's the next one."
Villa's narrow triumph was their third successive home win over West Brom in all competitions, with the visitors having only won at Villa Park once since 1979.
Albion are contesting their second quarter-final in eight years after comprehensively beating West Ham 4-0 in the fifth round, and reaching the semi-finals is high on Tony Pulis' agenda.
Tuesday's defeat ended a five-game unbeaten run for West Brom in all competitions, and was only the second since Pulis replaced Alan Irvine at the start of 2015.
The 57-year-old is hoping for much better from his side this weekend, having seen them waste chances to win the league match before Benteke's decisive spot-kick.
"It'll take me a couple of days to get over this," said the Albion boss. "But we have to dust ourselves down and come back and win a game of football on Saturday.
"We'll take Saturday's game as it comes. I'll have a look at what the squad is like and then go from there."
Saturday's clash is the first time the two sides – separated by 16 miles – have met in the FA Cup since 1998, with Villa hoping for a repeat of that 4-0 victory in the fourth round.
Dwight Yorke scored twice for Villa that day, but this time the focus will be on Benteke, as he looks to build on his first goal since January 4 and only his fourth of the season.
Villa are waiting on the fitness of defenders Ron Vlaar (calf), Aly Cissokho (groin) and Kieran Richardson (calf) after they all missed the league clash, but the hosts will definitely be without Alan Hutton.
The full-back received his 10th yellow card of the season with two minutes to play on Tuesday following a high tackle on Saido Berahino, earning him a two-match ban.
Berahino's fitness continues to be monitored by Pulis and his coaching staff, the striker having carried an injury going in the first game, with Brown Ideye also battling to be fit.
