No, you can not because they are for different consoles. This is true. The PS3 Bluetooth remote is not compatible with the PS4. As an alternative, you can try the Playstation app for mobile devices, which will sync and give you navigation and playback controls for PS4.

How do I connect my PS3 BD controller to my PS4?

Turn on the PS4. From your dashboard with all of your games, scroll up and to the right, then select Settings, represented by a briefcase icon. Select Devices > Bluetooth devices. Select DualShock 4 controller from the list.

How do I connect my PS3 Media Remote to my PS4?

It's possible to use the PS3 Media Remote on the PS4 *IF* you are using a Sony Television. All you need to do is to enable the HDMI media link from under the settings on the PS4. It is a little sluggish but if you don't feel like using the DS4, it's manageable.