Matthew 26:74

‘Then he began to curse and to swear, “I do not know the man.” And immediately the cock crowed.'

So he began to deny Jesus vehemently, reinforcing his words with oaths and curses. His denial had reached its ultimate depth. And at that point the cock crowed. In fact cocks would have crowed at various times through the night, so the point here is that this was the cock that heralded morning, and which he noticed. It was the one that had awoken his conscience.

There are no grounds here for suggesting that it was Jesus Whom he cursed. Had he done that it would surely have been brought out as being more than a denial. He rather cursed either himself, or some of those who were, in his view, glaring at him.