It wasn't that the battle wasn't close - it was. And well fought by both of them, but Achilles had lost. There were many reasons, flying through his head on his way out of the arena, leaving out a back door and going back to the apartment he had with Patroclus so that none would look upon Achilles the loser that night, for he was in horrific spirits and could not muster a good mood for anyone.
He was not used to fighting not to the death. When he'd single-handedly won the war at Troy he was not expected to stop before he killed anyone. He'd never trained with others; none could even see him fight, growing up. He was not made for these kinds of half-fights where you had to hold back and you could not kill. All that being said, all that being true, he had still lost and the shame of it rang through him.
He hadn't even gone to find Patroclus after the fight, but he was sure his beloved would know precisely where to find him and the state he would be in. Achilles could not sit; he paced, instead, running over and over in his head the fight and the moments of it that had led him to defeat.