Don't blame yourself, it was a game you play. Accident's happen all the time, and that's what this was an accident. The most important thing is he's OK, and it was you who got him the hlep he needed to be OK. Your fast thinking saved him! We all love our furbabies, and would never cause any harm to them.
I'm sure they know that. You take care, and enjoy the day with TeeJay.