No, you aren't the only parents to be surprised by feelings of loneliness and even depression after their children have left. Your lives have been focused on your children since before they were born, and suddenly those years are gone -- never to return.
God gave our children to us -- but we sometimes forget why He did so. The reason is simple: He entrusted them to us so we could train them and prepare them to be adults, to be out on their own someday. Yes, they gave us joy (and sometimes anxiety or heartache) -- but God didn't give them to us just for our happiness. He gave them to us so we could train them to be responsible and mature individuals. The Bible says, "My son, pay attention to my wisdom, listen well to my words of insight" (Proverbs 5:1).
And hopefully this has happened with your children. Take time to thank God for them, and for the privilege you had of raising them. Don't cling to them now, but do let them know you still love them and look forward to being part of their lives in the future -- but only a part. Pray for them also, that they will put Christ first and seek God's will in everything.
In addition, ask God to help you find new ways to fill the empty space you now feel in your hearts. For example, ask your pastor to suggest ways you can volunteer to help others in your church or community.