Abdullah Kurdi told the BBC he still hoped that world leaders could stop the war in Syria.
Haunting images of Alan's body lying on a Turkish beach a year ago focused world attention on the refugee crisis.
Alan's brother Galib and mother Rihan also drowned when their boat sank en route to the Greek island of Kos.
Abdullah Kurdi survived and now lives in northern Iraq.
He told the BBC's Fergal Keane that he thinks of his sons every day, but the first anniversary of their deaths on 2 September is particularly difficult.
The story of Alan Kurdi's family
Why Alan Kurdi's picture cut through
Did shocking image change anything?
"Every day I think of them but today I felt as though they had come to me and slept with me. This makes me sad again," he said.
"At first the world was anxious to help the refugees. But this did not even last a month.  In fact the situation got worse.  The war has escalated and more people are leaving.
"I hope that all the leaders of the world can try and do good and stop the wars, so that the people can go back to normal life."
After the tragedy, Mr Kurdi flew the bodies of his wife and children back to Kobane in northern Syria where they were buried.
In 2015, more than one million refugees and migrants reached Europe by boat from Turkey, but thousands drowned after being packed on to dinghies and overcrowded boats by people smugglers.
In March, a Turkish court sentenced two Syrians to four years in jail over the death of Alan Kurdi and four others.
Mufawaka Alabash and Asem Alfrhad were convicted of people smuggling, but acquitted of causing death "through deliberate negligence".
The EU has since reached a deal with Turkey that has stemmed the flow of people across the Aegean Sea.
However, thousands are still trying to reach Europe from north Africa, particularly Libya.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
The father of Alan Kurdi, the three-year-old boy who drowned a year ago as his family fled Syria, has urged Europe to keep its doors open to migrants.