"It was a big shock when the news came through, especially for the two players involved," said Bierhoff as Schalke 04's Julian Draxler and Benedikt Höwedes were passengers in separate cars during filming for Mercedes, one of the DFB's sponsors, when the crash happened.
An Italian police officer stands guard near the site where the accident happened. Photo: DPA
The accident at Germany's pre-World Cup training camp in northern Italy on Tuesday left a course steward in hospital and a German bystander in a serious condition.
The bystander was airlifted to hospital, while the course steward, named only as Michael K., is also being treated after he too was hit by the car driven by 19-year-old professional touring car driver Pascal Wehrlein.
SID, an AFP subsidiary, reported on Wednesday that the 63-year-old bystander is out of immediate danger.
Schalke centre-back Höwedes was Wehrlein's passenger in the Mercedes involved in the accident.
"Of course, the situation was a shock for me," Höwedes told the German Football Association (DFB) website. "I believe the images will stay in my head for a long time.
"Physically I'm fine, I could train in the afternoon after it happened, we were using seatbelts.
"The question is more: how are those injured doing? My thoughts are with them and their families. I hope they get better soon."
Höwedes said he had helped emergency services at the scene.
"I didn't do anything which anyone else wouldn't have done," he said. "To want to help in a situation like that is obvious."
Formula One driver Nico Rosberg, who was driving the other Mercedes car at the time of the crash, wrote on Twitter: "The accident shocked me, my thoughts are with both victims," while Wehrlein is said to be very upset by the incident.
Bierhoff said both players had spoken to the team psychologist before training on Tuesday night, while he visited both victims in hospital along with Rosberg and Wehrlein.
In an interview with the Hamburger Morgenpost, course steward Michael K. described how he spotted the bystander, thought to be a holiday-maker looking for an autograph from the German footballers, on the closed Alpine course.
"He wanted to take a picture and also get an autograph," he said, having suffered back, leg and elbow injuries in the impact.
"He wasn't on the road, but was right next to it, a few metres in front of the barrier.
"I shouted to him loudly. I wanted to pull him back, but didn't get to him in time.
"If it had taken two seconds longer, I would have been directly hit and I could have been killed."
Mercedes spokeswoman Claudia Merzbach said the event on the twisting roads was not a race and all video footage taken from within the cars has been handed over to police.
Both the DFB and Mercedes are in close contact with the families of both the victims and local police chief Johann Ramoser insisted there were no safety issues with the Alpine course: "The track was safe. That I can guarantee."
The DFB cancelled a scheduled practice match between Joachim Löw's World Cup squad and Germany's Under-20 side on Tuesday evening.
The DFB are holding their 10-day training camp in the north Italian Alps which concludes on Saturday before their first World Cup match in Group G against Portugal in Salvador on June 16th.