Welshman Davey added: "We're in the semi-finals - I've never been to Wembley.
"The players will be asking the chairman for new suits and bonuses now. But joking aside, they were magnificent. To beat a team like Chelsea is unbelievable."
Barsnley captain Brian Howard, who scored the winner at Anfield in the last round, said his side deserved the win.
"It hasn't sunk in yet," he said. "We knocked out Liverpool and have now turned over one of the best squads in England.
"The boys deserved the victory because of the effort they put in. We took our chance and now we're going to Wembley.
Who knows, it could be our year after having beaten those big teams
Tykes hero Kayode Odejayi
"You have to get the record books out to check when Barnsley last reached the semi-finals."
That was 1912 - a year which they went on to win the competition.
Goalscorer Odejayi was adamant Barnsley, four points off the Championship relegation zone, could win their second-ever FA Cup.
"It wasn't just down to me, the whole squad, the management and the fans deserve praise," he said.
"It's a magical tournament. Who knows, it could be our year after having beaten those big teams."
I want to congratulate Barnsley because they played very well,
Chelsea boss Avram Grant
Chelsea boss Avram Grant said Barnsley fully deserved their shock win.
"It's very disappointing, but I want to congratulate Barnsley because they played very well," he told BBC Sport.
"We didn't perform well in the first half but played better after the break before they scored their goal.
"It wasn't easy on the Oakwell pitch. We couldn't play our quick game and use our qualities. But I don't want to take anything away from their win."
Bookmark with:
What are these?