The Cottagers fell behind early when Royston Drenthe fired home with power and precision in the third minute but fought back when USA international Dempsey set up Bryan Ruiz, who scored his first Premier League goal with an exquisite chip in the 67th minute.
It looked like Fulham would run away with it but Ruiz was kept out by Dempsey’s fellow countryman Tim Howard late in the game before Bobby Zamora rounded the US keeper but was denied by the upright.
Former Cottagers striker Louis Saha then put the Toffees ahead in the 90th minute before Jack Rodwell added a third for the visitors in injury time, leaving Dempsey to reflect on a game of missed opportunities.
“We had two good chances, but we didn’t take them, and we got punished for it,” he told fulhamfc.com.
“[Even after conceding early] You just keep playing, believing in your football. We knew we’d get back in the game and we did. We had two really good chances late in the game, but weren’t able to finish them, and right after that they attacked, created a chance and they were able to take it, so that was the difference.”
Regarding Ruiz, he said it was great to see the Dutchman open his account in such style and admitted that Zamora was the victim of pure bad luck late in the piece.
“Yeah, we are creating chances, and it was good for Bryan Ruiz to open his account with his first goal,” added Dempsey. “For me personally, I enjoy creating chances, so I was pleased to get an assist today, so I’ll take that positive, but it doesn’t make up for the defeat.
“But of course, one consolation is that the goal will be good for Ruiz. It’s good for any attacking player. It gives you that little confidence boost to get things going, so it’s good for him.
“That’s the way it goes,” he said of Zamora’s miss. “Sometimes they don’t fall for you or go in as they should, and sometimes they do. Bobby does a lot for us, and he gets the goals, but sometimes you’re just unlucky.”