Just be honest with them. What you just said in your post is perfect. Tell them you decided to have an intimate wedding with a few relatives and friends. Tell them the reasons that you and your FI chose to do it, if they ask. But you really don't need to and shouldn't feel that you need to explain much at all to them. Most will understand and be okay with it. It's going to be hard for someone to take it personally, imo.
Now if you were having a large wedding and they were hearing about it but weren't going to be invited, that's a different story. But them knowing that it's an intimate wedding with those closest to you and FI should make it pretty clear and understandable that they won't be invited.
Alot of people choose to have smaller, intimate weddings. Don't feel bad about it, even if they invited you to their wedding. It's your wedding and it's perfectly fine.