To understand this intial meeting, it's important to understand the build-up behind it. Gatsby and Daisy knew each other in their past and had a short but passionate relationship. Since then, Gatsby has been planning to get Daisy back. He has created an image of her in his mind. The reason he even lives where he does is so that he can be closer to her. He has been planning this "meeting" for a very long time.
When Gatsby and Daisy first meet at Nick's house, it is incredibly awkward. Daisy was unaware that Gatsby would be there in the first place. Therefore, when she sees him, she is completely taken aback. Gatsby is incredibly awkward in this moment. He is uncomfortable and doesn't seem to know what to do with himself. The two just stare at each other. Immediately, Gatsby thinks he has made a mistake. He follows Nick to another room.
"This is a terrible mistake," he said, shaking his head from side to side, ' terrible, terrible mistake.
"You're just embarrassed, that's all," and luckily I added, "Daisy's embarrassed too."
"She's embarrassed?" He repeated incredulously.
"Just as much as you are."
When the conversation with Nick is over, Gatsby goes back to talk with Daisy. Nick leaves them alone for a while, and when he returns, he finds the two talking comfortably like nothing had happened. They are quickly able to restore the image of their past relationship, but Gatsby has glimpses of an idea that maybe the image he had built of Daisy in his memory was more than the real thing he has in front of him.