Nate was cut but it was far closer than some suggest. Conor definitely won the round, but look at what it cost him. He threw everything he had at a rusty Nate, and it wasn't enough. It isn't hard to win a first round if you throw everything you have into it, and most fighters are smart enough to avoid doing that. The problem is, most Conor fans are really new to the sport and don't understand that.
Nate had no sparring leading into the fight, the first round was it, and by the second he was warmed up he had Conor figured out, and finished him.
Nate didn't lose that first round by very much.