Horne went over for Warriors' fourth try in Saturday's 42-0 win over Lions to take his club total to 55.
"I think it will take a while to sink in, but it sounds pretty cool," Horne told Premier Sports.
"I started off my career scoring quite a few, but then I had a dry spell. However, since Franco Smith has come in, he plays a fast style of rugby that suits my game.
"Massive credit to the big boys tonight as the Lions are one of the most physical sides in the league.
"Now I can focus on other things. I am loving my rugby and I am so proud to represent this club."
Smith was full of praise for the new record scorer.
"He is through and through a Glasgow Warrior and scores some beautiful tries," he said. "He is a bundle of energy and it is a real pleasure to work with him. He understands the way we play."