The Premiership side needed to score after trailing 2-1 from the first leg of the third round tie in Germany.
However, despite having several clear-cut chances, Fulham could not find a way past outstanding Berlin keeper Gabor Kiraly.
Tigana told Sky Sports 1: “We had many, many chances, but not just today, also in the first game and I am very disappointed.
“The problem is one we have had all season that we could not score the goals and I did not have a striker on the bench to change things.
“If you have one chance, you have to score.
“I am disappointed, but it is the first step for the club and we have done very well in Europe and it is important to keep going.”
Tigana added: “You need experience and I hope today they have understood what is expected at a high level.
“If you want to keep going as a club, it is very important to play in Europe next year.”
Fulham now have a crunch Barclaycard Premiership match against Birmingham at Loftus Road on Sunday as they look to climb the table in their quest to secure a return to European football next season.
“It is a very different game, and an important game also,” reflected the Fulham manager.
“The league is our priority. Today we had many players injured, but I am happy because the spirit is very strong.”
FULHAM: Taylor, Finnan, Melville, Goma, Brevett, Djetou, Davis, Malbranque, Wome, Marlet, Boa Morte.
HERTHA BERLIN: Kiraly, Friedrich, Simunic, Rehmer, Nene de Brito, Goor, Marcelinho, Neuendorf, Hartmann, Dardai, Luizao.