The 31-year-old scored the only goal of the match as Derby secured an advantage ahead of the second leg at Craven Cottage on Monday night.
Jerome has said that the Rams 'would have taken 1-0' before the match, and branded the victory "a massive team effort".
"If you had given us that before the game we'd have taken it," Jerome told Sky Sports News. "It's half time in the tie so we can't get carried away. The boys were magnificent. It's a massive team effort."
Jerome has now scored five times in his last four appearances for Gary Rowett's side.