Strasbourg won 2-1, as Tyrick Mitchell's opener for Palace was overcome by goals for the hosts from Emanuel Emegha and Samir el Mourabet.
Chelsea loanee Chilwell said afterwards: “An incredible night. Having the full stadium, 35,000-odd people pushing us for the whole 90 minutes, they really pushed us through the game tonight.
"For a young group like this to show the fight that they says a lot about the groups and what the manager expects of us. We weren't happy with the draw - we wanted to go on and win the match.
“The manager told me to come on and - especially the five minutes before half-time - just settle the game down, just to get to half-time. Then we could talk as a group, regroup, go again in the second half. We knew before they scored that we were controlling the game.
"I'd say we were the better team. The second half was about trying to come into the game, help the team gain control back, settle the game down and build from there. That's what we did."
On being senior the player at 28, Chilwell added, "I'm thriving off it, to be honest. I'm really enjoying what's expected of me as a player on the pitch. They're a young team, of course, and full of exciting talents and so much youthful exuberance.
"But I feel like as the older, wiser head, it's my responsibility sometimes just to settle everyone down and manage expectations."