In canon, he doesn’t see the thestrals until after he sees Cedric die in book 4. Before that, he always refers to the carriages as ‘horseless.’ I guess he either didn’t have direct line of sight to his parents being killed, or it was so long ago that he didn’t really remember.
"Harry, Ron, and Hermione followed the rest of the school out onto a rough mud track, where at least a hundred stagecoaches awaited the remaining students, each pulled, Harry could only assume, by an invisible horse…" Prisoner of Azkaban, “The Dementor,” page 98 in my copy (the Canadian edition by Raincoast Books in 2004)