You didn't say whether these were your users or external users, nor the Exchange version. My links are 2007 because that's what I support, so I had them lying around my bookmarks.
By default Exchange is set up with integrated security (using the logged-in user's AD credentials). Your app presumably doesn't have any, or doesn't pass them. This is a common thing.
For internal users: You should be able to just approve the server IP address as always allow, yes. At that point, it's possible that Exchange will flag the mail as spam. If it does, you might have to bypass the content filter for the application sender address, but it's less likely than in the case below.
For external users: You'll need to set up a new receive connector just for your app. Ordinarily I'd copy and paste the relevant bits, but TechNet has a pretty walk through with pictures and everything that's probably easier to follow than what I would come up with. Also, see above about flagged as spam/bypass the content filter for sender address. If what you're sending looks "spammy"--no message body, attached PDF, and the subject line "Invoice," for example--you'll almost certainly have to do this.
If you're running 2010 or 2013, hopefully this is enough to at least point you in the right direction.