He heard the protesting sounds but didn't stop putting pressure on the wounds. He'd hold the shirt there for a few seconds, check underneath, and replace it. This cycle continued for a few minutes until he was positive that the bleeding had stopped, though the sight of it still worried him. He tossed the shirt away and let go of Sirius' arm.
"People say things they don't mean. When they're angry or upset," he shrugged, looking away and down at the floor because he felt like he had to look at something else. Not that Sirius was likely to get the double meaning behind his words because he was so far gone. Remus himself was pretty drunk and tired, and even more tired because he was drunk. He sighed and started working his way under the covers until he was lying next to Sirius. Almost instinctively, his head pressed into Sirius' neck, giving another, "I'm so sorry," though he wasn't sure if he'd be heard or not.