Clint Dempsey's hat-trick helped a strong-looking Cottagers side avoid a potential third-round upset against the League One leaders.
The United States international's efforts were complemented by a late Damien Duff goal as Fulham secured a 4-0 victory and safe passage to the fourth round, much to the delight of Jol.
"I wasn't here for the last four or five years but I still think the FA Cup is the best competition in the world," the former Tottenham manager said.
"I told the players that and maybe they think differently, but I don't think so.
"For a club like Fulham, maybe you can discuss about [the importance of] the Carling Cup but the FA Cup for me is not sacred, but it is one of the best competitions.
"The only thing that is amazing is I looked at Birmingham v Wolves, for example, and I said to Ray Lewington 'I thought it would be a sellout?'
"Even when I played it was a sellout and it was the same when I was at Spurs.
"20,000 is okay and I hope and that appreciation for the FA Cup will remain the same."
Fulham got off to the best possible start against Charlton as Dempsey flicked home the opener in the eighth minute.
Boosted by up to 7,000 visiting fans, Charlton attacked with intent and only fine goalkeeping from David Stockdale prevented an equaliser before Dempsey and Duff settled the tie.
"In hindsight 4-0 is a very good result, especially if you see the other results," the Dutchman added.
"We knew before the game they have got a very good side with a good mentality.
"They win games and make a habit of that. They had two defeats in 24 games and that showed in the first 15 minutes of the second half.
"When you let them play to their strengths they are a hard team to beat, but of course we have got out qualities as well.
"The first 25 minutes was really good from us but the only thing we lacked a bit was end product.
"When we made the substitutions in the second half, we scored immediately with Clint playing on the inside.
"Damien Duff did very well when he came on. Everybody stepped up a gear and we realised that we had to take it to them to win.
"It was very positive that Clint scored three goals and Bryan Ruiz created all the goals."
While disappointed by the scoreline, counterpart Chris Powell was pleased by Charlton's level of performance at Craven Cottage.
"I think what today shows you is that you have to be clinical when you get the chances," Powell said. "That is the difference.
"A couple of the goals came through deflections and perhaps a penalty that shouldn't have been.
"I feel 4-0 was quite harsh on us today because we did have moments of quality and chances.
"I thought David Stockdale made three or four very good saves from Bradley Wright-Phillips, one from Yann Kermogant and one from Danny Green.
"They are the moments when you play a team from the higher levels you need to take.
"But Fulham are a very good team. They kept possession very well and have some good, good players.
"I felt we did as well as we could do and the scoreline does not really reflect what happened today.
"It was a one-off game that we earned the right to be here after winning in the first two rounds, but it is more about the 22 games that remain for my football club now."
