Compliments are one of the easiest ways to put people at ease. If someone is selling an item they were probably fond of it at one point. Look for opportunities to compliment the person you are bartering with or the item you want. One important caveat is that the compliment does need to be sincere.
People will be put off by false praise. At the end of the negotiation you can compliment the other person’s bartering skills.
This is far more effective in building a lasting relationship than telling the person you would have paid more for an item, which will likely make them resentful and negatively impact future sessions.