Fulham needed a Hugo Rodallega equaliser three minutes from the end of extra-time to send the tie into a shoot-out, where John Arne Riise scored the decisive penalty.
Jol's men had looked comfortable with the first-half lead given to them by Adel Taarabt but Jack Dyer equalised after 85 to send the tie into extra time and then substitute Michael Symes put Burton in front.
"It could have been a bad night for us," said Jol. "The crowd smelt blood but it turned out nice in the end.
"We put a strong side out because we wanted to win the tie. In England the lower league sides make it difficult for you, and they made it difficult for us.
"We had all the play for about 78-80 minutes but then towards the end and in extra time they had their spell.
"But I am pleased with the resilience of my squad, they showed that they wanted to get through.
"I was impressed with Burton, they are a good side. They have a great home record, I think it was the best in their division last season.
"I wish them all the best for the remainder of the season, I think they will do very well."
Burton boss Gary Rowett was proud of the showing of his team, saying: "I thought we had some brilliant performances.
"To almost knock them out was incredible. I thought we were brilliant, absolutely brilliant.
"We've got a brilliant group of players here and over 90 minutes we are still technically unbeaten this season."