Hayden was ruled out of the upcoming campaign with a torn hamstring that he picked up during a training session on Saturday.
Conte revealed that none of the defensive line thought that the injury was so severe at first, but hopes that Hayden will return to the side as soon as possible.
"Kelvin has worked so hard. He's been doing a great job, and it's really tough to see him go down like that," said Conte on the team's official website.
"I know none of the [defensive backs] really expected it to be that serious. To hear he's out for the whole year is kind of shocking. So prayers and thoughts go to him and his family, and hopefully surgery goes well and he's back soon."
Hayden's spot is likely to be filled by Isaiah Frey, but the second-year cornerback was more concerned with his teammate's well-being than any opportunity to get into the side.
"You hate to see that happen. I'm praying for him that he gets healthy really fast," said Frey.
Hayden's injury is the second blow for the Bears during their pre-season having already lost defensive end Turk McBride to a ruptured Achilles.