Mark Robinson lost his life when he fell and was struck by a recovery vehicle during the transportation of Gutierrez's crashed Sauber to the paddock.
"All the drivers in F1 appreciate the work of the people involved," said Gutierrez at Silverstone on Thursday.
"In this case it was a person there purely because he loves racing, and it's really admirable having these kind of people working and helping us make such great events, and they are a big part of it.
"I really give my biggest condolences to his family. It was not the best feeling to hear about it because it was someone working with all of us on an event."
Gutierrez said it was important to learn about safety lessons from the incident, but admitted some danger was inevitable in all elements of motorsport.
"Racing is dangerous and we all find ourselves exposed to that," he said. "We have to take the right measures to be safer and safer, in all aspects.
"It's hard to put it into perspective. It's a situation no one can control."