In the post-conflict phase, no matter how it was resolved, emotions and states remain, most often anxiety, distress and anger, which have negative consequences for the person concerned, but also for the relationship with the other person. If the relationship has not broken down, it needs to be repaired so that the remaining tension does not lead to new differences or, later, to the dissolution of the relationship.
The most important tool you have at your disposal is effective, honest communication. Let go of your ego and confess your part of the blame, apologize, then express your desire to make things right, and at the same time acknowledge that the person and your relationship with them are important to you. If you are not the one at fault, although this is debatable because it takes two to be right and still two to be wrong, then just as openly start a discussion that diminishes or erases the negative emotions of both you and the other person. "I'm sorry for what happened between you and I, the situation has affected me and I would like to discuss it to prevent a repeat of the incident. I would like us to continue to remain on good terms." Remember assertive communication (see " Conflict prevention").
Whoever is guilty, the first step needs to be taken quickly, clearly and well. Pride is the biggest enemy you could have right now. If you accept it, it will prolong the bitter aftertaste of the dispute, regardless of who took the blame.