Neb. Rev. Stat. § 14-807

In all cases of damage arising under the provisions of sections 14-101 to 14-2004 , the party or parties whose property is damaged or sought to be taken by the provisions of such sections shall have the right to appeal from such assessment of damages, but such appeal shall not delay the appropriation of the property sought to be taken, delay the improvement proposed, or retard the change of grade sought to be made. In no case shall a city of the metropolitan class be liable for the costs or interest on such appeal, unless the party appealing shall be adjudged entitled, upon the appeal, to a greater amount of damage than was awarded. The remedy by appeal allowed by this section shall be exclusive.