No you did nothing wrong. It is no different than going into a store and seeing something on sale and going home to think about it. It isn't the store's responsibility to let you know if someone else has shown an interest in the item or worse yet bought it. When you go back and it isn't there well you just have to live with missing out.
In daycare it is the same. I am advertising to fill a space and some weeks I will do 3-4 interviews for the same space. The first family to get back to me with completed forms and deposit generally gets the space.
At the same time I am interviewing families just as much as they are interviewing me and I am not compelled to accept every family that comes into my daycare. That is the joys of being private. We can take the overall status of our group into consideration so that the new family will fit in with ages, hours, expectations.
When a family starts expressing concerns such as the cat right at the interview it is what we call a "red flag" and makes us think very carefully before accepting such a family since the complaining and expectations tend to get worse than what was expressed at the interview.
One a family has signed on, I have gone back and sent emails to families that I thought might still be considering me and told them the space had been filled but it is not a requirement. Mostly if it happens within the week of interviewing I send an email but if more than a week has gone by I don't always send an email and assume the family has made other arrangements or well they took too long so they lose out.