The loss of Anatolia wasnt due to the Normans, the Normans undoubtedly impeded early efforts to recover Anatolia but the damage was already done before Alexius came to the throne. After Manzikert Anatolia was wide open to thousands upon thousands of Turks to settle in, early incompetance made a bad situation far far worse, as much more land than was necessary was lost.
The Normans threatened to take over the Balkans, the lose of the Balkans and Anatolia would surely have killed the empire off there and then. The Byzantines suffered several defeats first by Guiscard and then by Bohemund, but ultimately the Normans were expelled.