At least 110 people had attempted to crowd onto the same boat, with a larger group attempting to join at the last moment as French police tried to prevent the boat leaving, the BBC reported.
Speaking to the broadcaster, Mr Alhashimi said: “I could not protect her. I will never forgive myself. But the sea was the only choice I had.”
In the stampede, Sara was suffocated, while Ahmed's wife, Nour AlSaeed, and their two other children, 13-year-old Rahaf and eight-year-old Hussam, were also trapped in the boat, but still able to breathe.
“That time was like death itself. We saw people dying. I saw how those men were behaving. They didn't care whom they were stepping on - a child, or someone's head, young or old,” he said.
“People started to suffocate.”
It was only when French police reached the boat that he was able to reach his daughter, he said.
“I saw her head in the corner of the boat. She was all blue. She was dead when we pulled her out. She wasn't breathing,” he said.
The family were attempting to make the crossing for the fourth time, and had been staying with a relative in Sweden.
However, they were told that they were going to be deported from Sweden to Iraq, where Ahmed had fled due to threats from militia groups there.
The family are now waiting to bury Sara’s body, he told the BBC.
French officials said the others killed in the stampede when the vessel left at 5am near the Plage des Allemands were three men and a woman.
The Calais prefect, Jacques Billant, told the Guardian that despite the deaths, 57 people had attempted to continue their journey to Britain once the boat’s motor had been restarted.
The deaths came hours after Rishi Sunak’s government passed legislation to allow it to deport asylum seekers who arrive in the UK on small boats to Rwanda.