Lieberknecht's men are bottom of the table going into their final game of the campaign against Hoffenheim and are two points adrift of Hamburg in 16th.
Braunschweig require a victory at the Rhein-Neckar Arena on Saturday, then hope Mainz and Schalke do them a favour against Hamburg and Nuremberg respectively if they are to have any chance of avoiding an immediate return to the second tier.
Lieberknecht is backing his side to secure the relegation play-off spot and believes neutrals are behind Eintracht.
"We will have a lot of sympathy on our side. Maybe except for two cities, Hamburg and Nuremberg, it is such that the whole of Germany is keeping its fingers crossed," he told SportBild.
"We are aware of our sympathies as an underdog. It's just the way it is that people have sympathy for a supposedly smaller traditional club."
Having given themselves hope of avoiding the drop with a 3-0 win over Hannover at the start of April, Braunschweig have since lost all four league games.
While they face a tough task to escape the bottom two, Lieberknecht has vowed to fight to the end.
"We will try again to achieve something seemingly impossible," he added.
"The situation is still exactly as is - as we had predicted. It takes until the final week for a decision to be made - and that we are there, is a very good story."
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