Chilton lined up as Marussia's only driver on the grid in Sochi a week after the team had been devastated by the serious head injury sustained by Bianchi when he crashed into a recovery vehicle at the Japanese Grand Prix.
Bianchi remains in a critical but stable condition with a diffuse axonal injury but Marussia opted to race on Formula One's debut in Russia, although Chilton could only finish nine laps before retiring with a suspension issue.
Despite not being able to complete the race, Chilton praised the efforts of the team and the support of the fans.
"After an incredibly tough week for everyone in the ream, we all deserved so much more from today's race," Chilton said.
"It hasn't been an easy day, far from it, and all the guys have had to dig deep to get us to the grid.
"When we got there of course, it was very emotional with all the support for Jules. I think the team, the sport and all the fans have really done him proud.
"What the team needs now is to head home for support from their families and colleagues back at the factory. Somehow we need to find the strength to regroup and move forward, which is hard to contemplate right now."
Chief engineer Dave Greenwood echoed Chilton's sentiments and indicated that Marussia will need to look into replacing Bianchi in the three-week break before the United States Grand Prix in Austin.
"This is not the race outcome we were hoping for, but I think we can be justifiably proud of the way we have pulled together this weekend," Greenwood said.
"We have taken huge encouragement from the tremendous support shown towards Jules by the entire F1 community and for that we are extremely grateful.
"We hope that it has helped Jules' family at this difficult time. At some stage we will need to look ahead to the remaining races of the season, but for now, we’re pleased to be heading home."