No, you must never import private keys when dealing only with trust. Keys are used for encryption/decryption, not for trust. In this case it seems you're using a self-signed certificate for F5 management, so it's like a special case of a Root CA establishing the trust for itself (by definition, a Root CA is self-signed).
But... reading between the lines in your question makes me believe things are not working yet. Or are they?
If not, I would suggest the procedure in my previous post: get a traffic capture, confirm the certificate your java machine is getting from the F5 box is the one you are expecting to see there. Or in other words, if that certificate is signed by the one you have imported into java trust store.