All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His Slave and Messenger.
If you failed to assume Ihraam from the Meeqaat (the place from where one assumes the state of Ihraam) for any reason, be it due to sleep or anything else, then you have missed one of the obligations of 'Umrah. If you had assumed Ihraam after having passed the Meeqaat, then you have to sacrifice a sheep and distribute its meat to the poor within the sanctuary (Makkah); this is an expiation for missing an obligation. However, your 'Umrah is valid, Allah willing, if you had performed all the pillars; Ihraam, Tawaaf (circumambulating the Ka'bah) and Sa'y (walking between As-Safa and Al-Marwah). The prominent scholar As-Shinqeeti said in Al-Adwaa': "You should know that the majority of scholars are of the view that whoever passes one of the Meeqaats without assuming Ihraam while intending to perform the rituals (of Hajj or 'Umrah), then he has to offer a sacrifice." His evidence in this is the narration of Ibn 'Abbaas: "If someone forgets any part of the ritual or does not perform it, then he has to slaughter an animal." The scholars said that whoever passes the Meeqaat without assuming Ihraam while intending to perform the ritual, then he has abandoned part of the ritual (of 'Umrah); in such a case, he is obliged to sacrifice an animal.
Allah Knows best.