The United States international's hat-trick yesterday helped the Cottagers avoid a potential upset against Charlton in the third round.
Dempsey's goals along with a Damien Duff effort helped Martin Jol's side to a 4-0 triumph in a London derby in which the npower League One leaders' performance belied the scoreline.
"It was good for us to get the win," Dempsey said after the match.
"It's the first time I have got a hat-trick in my professional career so that was good as well.
"Hopefully we can go on a nice run in the FA Cup and keep doing well this season.
"You have to take one game at a time.
"It's the luck of the draw so it depends on what teams you get and whether you are playing home or away. That comes into it.
"What will be will be. We will just take it one game at a time and, if we play the football we know we are capable of, maybe we can go all the way."
Dempsey has become part of a potent attacking triumvirate alongside Moussa Dembele and Bryan Ruiz.
Fulham struggled for goals at the start of the season, but the Texan believes their change in fortunes is thanks to their time together.
"We have been working on different formations and learning how to adapt to our opponents," he said.
"We have not just been playing one style and we are getting that understanding [together].
"We are trying to create as many chances as we can and scoring goals and hopefully that will continue."
The scoreline was cruel on the Addicks, who were cheered on by up to 7,000 visiting fans at Craven Cottage.
Charlton attacked with intent and only fine goalkeeping from David Stockdale prevented them netting an equaliser.
Yann Kermorgant, Danny Green and Bradley Wright-Phillips were all denied by the England man, before Fulham put the game beyond doubt.
Bradley Pritchard was one of Charlton's standout performers by the Thames and was proud of his team's display.
"I am disappointed obviously," he said.
"I thought we played well in spells and were not too overawed by the atmosphere.
"I thought we started the second half well and tried to put them on the backfoot.
"But they are a Premier League team and if you give them any chances, they will take them.
"We had a couple of chances and we didn't take them and unfortunately that is just the way it goes.
"We don't think the result reflected the performance, but if you give a Premier League team chances they will punish you.
"4-0 does not reflect it but you have to take it on the chin."
This time last year Pritchard was playing for non-league Hayes and Yeading in front of few more than 250 fans and was quick to praise Charlton's visiting support at Craven Cottage yesterday.
"They were fantastic, they really were," he said.
"They kept us going, especially when we had the good spell.
"I thought we would at least get something then and they were our 12th man.
"Unfortunately, I think we needed a 13th or 14th man to stop Fulham because their movement was fantastic."