So I am sure this seems like a stupid question as I know cat bacteria is most likely harmful to frogs. However, I am trying to figure out the likelihood of my two American green tree frogs having died because of cat bacteria.

I had these green tree frogs for a few years. They were both rescues and so their actual age was unknown. They did come from the wild, both were hit by vehicles. I saved them, took them to the vet and nursed them back to health. I was told not to re-release and so I have had them for a few years and was quite attached to them.
I foster animals and never until recently had a problem with the foster cats bothering my tank critters. Well, right now I have a devil cat. His previous owner was incompetent and was going to have him put to sleep at only 9 months old because of behavioral problems. However, he was taken from his mother at only 4 weeks old, kept isolated for his whole life from other animals and people (so never learned how to properly behave) and was declawed (which has made him more apt to freak out when cornered); so I can see where his problems originate from and knew that he could be rehabilitated and saved. He behaves much better now than when I first got him but he still has issues including pestering my tank critters.
I do my best to keep him out of the room I kept my frogs in but he is amazingly sneaky and I would find him sitting on top of my tank frequently. He even broke into my cricket tank a few times.
I've managed to keep him out of that room for over a week now and my frogs didn't show any signs of being sick but they just suddenly died within a day of each other. They were kept the same way I've always kept them as I was told to do by the vet I saw. Distilled water, 2-3 large crickets daily each (more of less depending on their appetite), D3 and multivitamin provided, room kept between 70-80 degrees, just a basic light, kept in a 10 gallon tank.
As they were rescues, I don't really plan on getting more but I am pretty bummed out. I just want to know what the possibility of this cat having shed bacteria from his paws into the tank and killing my frogs. I can't do anything now for my guys but I would like to have at least a guess of why they died.
I feel awful that I may have indirectly caused their deaths. If anyone has had a similar experience or any inclination of what could have happened, I would love to hear it.

Thanks!