Sorry; you'll need to contact each organization and provide new credit card information. (Ideally, you should have done this before canceling your card.)
Unfortunately, there's no easy or "bulk" way to do what you seek, unless you used a single intermediary (e.g. PayPal) in the first place – and that's not an approach I would recommend due to fees and other potential issues.
I've been through this process twice before – once for having cancelled an account, and once because my account number was changed due to credit card fraud – and contacting each organization having a recurring payment was a necessary hassle each time. :-/
But, I did find one way to save time: My approach was to handle anything considered a bill myself and as soon as possible, so a payment wouldn't be declined and potentially harm my credit. I either called each vendor by phone or used their secure web site, when possible.
Since I wanted to minimize my time on the phone or writing letters, for charities I decided to let them get around to requesting my new account details. Each quickly noticed a declined payment and wrote to me to request updated account information. I just had to fill in whatever form was provided and send it back, which saved me time. Many of them have a streamlined process for this because credit cards expire all the time. Still, if you want to save them the hassle, the letter, and the stamp, then do call.