TL;DR No, you can't.
No tax jurisdictions let you claim a tax rebate for your time.
Here is a reference for the specific case of the USA.
There are two reasons. First, if they did this for you, they would also have to do it for everybody who volunteers their time for a charity, in any capacity. That would cost billions of your currency unit. Second, it's far too easy to scam. Someone shows up at a charity, does something completely pointless for a few hours, the charity certifies that they did it, and the person claims money from the government.
The exception here is if the product you donated is something you sell on a regular basis. If that's the case you might be able to claim it as a donation of goods, for the price you would normally charge - although there are probably some other hoops you need to jump through first. For that you absolutely need to tell us where you pay your taxes.
I would recommend instead spending a little time basking in the knowledge that you have contributed to the ongoing good of humanity. That's a reward they can't deny you.
What about actual costs?
Actual money you spend is a different matter. That's definitely going to need knowledge of your specific tax jurisdiction. Probably the best way to do it is to have the charity pay for those costs directly to the server providers (I'm assuming its only a few tens of dollars a month) and for you to make a monetary donation which covers it. You would get a rebate on the donation. You need to make sure there is no suspicion that any of the money you donate is coming back to you.
A completely irrelevant aside
Have you thought about what will happen if you aren't in a position to support this system any more, especially if you were to die or get sick unexpectedly? If you want the charity to keep benefitting from your work you should make sure that they have access to your code and the servers.