Unfortunately Apple uses the same term "Apple ID" in two different contexts and it can be very confusing.
If you simply changed the Apple ID = email address for the account, make sure the device can connect to the Internet so it gets that updated information.
If by "Apple ID" you mean you set up a new account, that can be more difficult. You are encountering this feature or a related service:
'Activation Lock for iPhone, iPad, and iPod touch' is a security feature that's designed to prevent anyone else from using an iPhone, iPad, or iPod touch, if it's ever lost or stolen. To learn more click here --> http://support.apple.com/HT201365
For an individual to remove an activation lock absolutely requires the information for the account that applied the lock. Click on this link to learn 'How to remove Activation Lock' --> https://support.apple.com/HT201441
Here are additional resources if you are the original owner:
Help with a lost Apple ID or password:
• "If you forgot your Apple ID" [this is likely an email address you are using or used in the past] click here --> https://support.apple.com/HT201354
• "If you forgot your Apple ID password" click here --> https://support.apple.com/HT201487
Reset device:
Apple can completely reset a device if a person can provide sufficient evidence of valid ownership. This is done online at: Activation Lock support request - https://al-support.apple.com/#/additional-support Apple says, "Proof of ownership documentation is required," but does provide details as to what is acceptable proof. Prior to this new online service Apple typically required the original receipt issued by Apple or an Apple Authorized Reseller and documented provenance (so typically it would be the original owner who does this, or a descendant with legal proof of ownership).