Is it actually r*pe?

I was with a guy at a party, we had been on a couple of dates before and knew eachother so the plan was to go to the party together and them crash at his uni acom after. I get quite drunk and we start heading back to his flat. I’m seriously intoxicated at this point. When we get back to his flat i remember asking him ”Is it okay if i dont want to fuck you?” and he says something along the lines of ”ofcourse, thats not why im here” i go ”cool cause i dont want to” and i lay down in his bed. I think i fall asleep because i have a gap in my memory, but i wake up to him touching me and stuff. I don’t say no or do anything to stop him so we end up having sex and going back to bed. On the way back the next morning i was crying thinking i should have said no. Today it hit me that it could tecnically be rape? But i hadn’t reflected on it like that before. I’m not sure though? is he in the wrong?

Since there seems to be confusion let me clear it up: - When i say i ”fell asleep” i mean for maybe 10-20 min as i was still very drunk when i woke up to him touching me - I was too tired/ drunk to really say anything or do anything or i just didnt care i dont remember but i just kinda stayed still and layed there - I had told him i didnt want to beforehand but not during the act

UPDATE: i confronted him about the situation and he confessed and apologised. He said that he was in fact drunk, but not drunk enough for it to excuse his actions and that he did infact assault me. I’m not going to report the crime.