I don't think Drogon saw him stab her so he might not have known it was Jon, he appeared just after, probably sensing she was dead, I shed a few tears!! As Jon Snow is a Targaryen maybe the link with dragons stopped him from being killed.
It seemed quite poignant that he went for the Iron Throne, the drive for which helped send his mother mad and linking back to breaking the wheel. I think, anyway.
Also them not wanting to kill Jon Snow off given he was a big part of the final scenes, and it meant we got to see Tormund again, which I was glad about.