Team Sky's star fell while training on the 9.7-kilometre time trial course around the old city. Around four hours later, he began, looking much better but with blood still visible on his right side.
"I am glad it wasn't more serious. I am glad I was not more seriously injured," Froome said after cooling down at Sky's make-shift camp on a Jerusalem side street.
"My body's not too bad. Crashing always hurts, but it could have been worse."
The first stage ended when Dumoulin, the Dutchman who ended the 2017 Giro d'Italia in pink, finished stage one two seconds ahead of Rohan Dennis (BMC Racing).
Froome had already come through, climbing the last 300 metres to the line and finishing at 12-39. Classification riders Simon Yates (Mitchelton-Scott) and Thibaut Pinot (Groupama-FDJ) also rode faster, with Yates clocking a time 20 seconds slower than Dumoulin, 17 ahead of Froome.
"A 37-second loss? There are a lot of classification riders thereabouts where I am. Rohan Dennis and Tom were the two guys who made the most of today. It's a long way to go still. It feels good to be racing," Froome said.
Froome said he did not come to Jerusalem expecting to win the opening stage. "No, no, not at all. I am not relying on time trials to win this Giro. Tom did a great ride today so to win like he did today was impressive, so chapeaux to him. He is the world time trial champion, so I am not too surprised by him."
The ride might have put Froome in 21st place, but 20 stages remain and he appeared fluid despite the road rash down his body. The riders starting the 101st Giro only had Friday morning to test the course.
"I just lost the front wheel on a corner. I was testing a corner at race speed. A crash is always going to hurt, and it's not an ideal way to start a race with a crash. It's all part of the sport," added Froome.
"It's only superficial cuts. I was probably braking around a corner and turning at the same time, and the front wheel went."
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