Of course, Jed couldn't bring himself to say something as far as that. It was not because he did not regret it, but because he had already a sense of guilt that would come after he admitted it. He even wanted to beat himself hard for that.
Eckart was his closest friend in the world, with whom he grew up with before the emperor could learn how to walk. Although he didn't know why their parents made sure that they both grew together, there was a clear reason why Jed trusted and followed Eckart now.
Eckart was a great prince. In Jed's eyes, there was no other legitimate ruler than Eckart during his time, and he was also the only ruler who could rule Aslan most fairly and greatly. Rather than living the life of a wealthy and peaceful bystander only for himself, Jed had firm conviction in the emperor that allowed him to be his close advisor, thus facing the harsh political realities.