After karna’s death, kunti revealed that karna was actually his son and pandavas eldest brother. Arjuna didn't spoke anything right after this revelation. He just silently listened to his mother’s words. It was yudhishthira who expressed his sorrowness after learning the truth.
This are the words expressed by yudhishthira to his mother.
Oh Mother! Till now I have had enormous respect for you! However, you’ve committed a great blunder of not revealing Karna’s identity to the world, just because of your selfishness! You’ve not spoken a single word about Karna all these years to me, nor to Arjuna, nor to Bheemasena or any one of us! Had you informed us of Karna during our childhood and early days, I would have ensured that Karna never slept for even a single day at Duryodhana’s! Had you atleast informed us of Karna before the commencement of the war, I would have gone and personally convinced Karna to come to my side – Or, even if that would not have been possible, I would have ensured that Karna was alive today! Ultimately, Karna had to meet his end because of Arjuna and myself and I’ve to take the blame for the entire fiasco! Had you disclosed about Karna at an appropriate time, the entire disaster could have been averted! Karna could have led a dignified life!”
Yudhishthira was deeply moved away by the truth and thus he cursed all women.
Oh Kunthi Devi! Unable to bear the loss and separation of my elder brother Karna, I’m hereby inflicting a curse upon you, knowing the fact that you are my own mother! However, the blunder that you’ve committed all through your life should not go unpardoned! I’m hereby cursing all of womanhood including you, that secrecy will never stay in you forever! You will not be able to maintain any secrecy in any aspect of your life! Just because you had concealed Karna’s story within you and made Karna a victim to the outside world for no fault of his, you will henceforth never be able to maintain any form of secrecy in your life!”
Later, arjuna felt intense guilt and remorse for killing karna in the battle. He later took great care of karna’s son vrishketu and helped me to emerge as a brave warrior like him.
Unfortunately, modern shows like mahabharata (2013) and suryaputra karna (2016) misinterpret the actual events like after the final duel karna was alive for a long period enduring the unexplainable pain.He attentively listened to his brothers queries, showed them a proper direction and even convince arjuna that he did amazing job by defeating him & pat his back for doing so.
And one more thing is duryodhana begging infront of everyone to save karna’s life, especially they show that he felt to krishna’s feet for his dear friend.
There is no doubt that duryodhana was a good friend to karna and he completely shattered by his demise.It broke him more than losing all his brothers, even dushashan’s death not made him feel like that way.
He knows that his defeat is inevatible after karna’s death and have no hopes like it was earlier. But, he is not that weak or humble enough to beg infront of his enemies to restore his friend’s life by offering them his own.