A second-half strike from Nils Petersen consigned the Premier League outfit to defeat at the Weserstadion, with an effort from Na Bangna the closest the visitors came to restoring parity.
But, with games against Real Betis and Parma still to come, the Dutchman has promised his team will be better when the 2013-14 campaign gets under way.
"They are a good team - not the best team in the Bundesliga - but normally they play at home and they are good," he told the club's official website.
"Over the past six months or so they have struggled a bit and we would would have liked a better result against them, but it was probably our first real serious test and we to Austria now and have to put a few things right.
"There were too many gaps between defenders and midfield and up front. We need pace and a little bit of quality.
"[Dimitar] Berbatov was good, but he can't do everything and we needed to get in behind.
"Today we looked a bit rusty from the start. But I can forgive the players at this stage as we will go to Austria and work hard, train hard and we will do something in the transfer market and be totally different by the start of the season."
Fulham were also dealt a blow when midfielder Alex Kacaniklic left the field with a hamstring injury, and Jol has revealed that the Swede could now miss the start of the Premier League season.
"He [Kacaniklic] had to come off with a hamstring injury," he continued.
"Hopefully it is not too bad, but he may be out for a couple weeks. That is not what you want from pre-season, as you want to go to the camp with all of your players fit."