In July last year, the UK ISPs called for the High Court to launch the review, stating the Act was "rushed through" and had "insufficient scrutiny". The two firms were also concerned that measures to tackle net piracy - including plans to temporarily suspend people from the web - could be in breach of "basic rights and freedoms".
However, the judicial review, which began in March this year, rejected four out of the five claims put forward by the ISPs.
"Both companies believe the High Court's conclusions on many of the other important and complex issues put before it were not robust enough to provide the certainty and clarity which the companies sought," the ISPs said.
The pair want four of the five grounds addressed in the initial High Court case looked at again, as they believe the Act is not consistent with a number of EU directives including the EU's Technical Standards Directive, the E-Commerce Directive and the Privacy and the Electronic Communications Directive.
"Quite apart from the potential impact on their businesses, BT and TalkTalk believe the DEA could harm the basic rights and freedoms of ordinary citizens. Many MPs of all parties, consumer groups and other communications providers share this view," the pair added.