The Glasgow prop said while pointing to his phone: "It's not stopped buzzing. A lot of people were really happy on the text messages, which I was really proud to receive. I need to try to text them all back later this week as well!"
Moray earned his first two Test caps as a replacement during the Six Nations but those cameos had nothing on the feeling of starting an international for the first time.
"Obviously, I had to keep focused on the job in hand but it was really emotional running out and playing," he said.
"When you pull on the jersey and start, it's just fantastic."
He added: "I felt I started well, got hands on the ball early and I was happy enough with the set piece.
"I had the family there to watch as well and was really pleased to go out there and play the full 80.
"I was struggling towards the end - it's quite tiring - but really happy with the win."