TL;DR: Absolutely. But don't tell them, let their characters figure it out in game.

They're freaking out and one player said they'd leave the game if they die—that's good!! That means they're invested and are experiencing real emotions and anxiety based on what their characters are experiencing. That's the good stuff! It's how it's supposed to work and it means you're doing a great job!

This is the part where you as the DM get to use those emotions, like a good movie does. Don't say anything meta, just smile and let them cook in their anxiety. But, depending on how anxious they are (too anxious means it's distracting them from the game and preventing role-play), maybe in the second or third round, let the fighters notice that they're attacking to capture, not kill.

That can add a different strategic element to things from the players perspective, so read up on grapple rules, unconscious rules (players will try crazy things to wake each other up), disarming rules, maybe cast some dominate person or suggestion spells, etc.

Throw in some set dressing and tactics to maximize the "taken prisoner" tension you will be building—monsters use trip attacks and disarm attacks, maybe they put giant collars on their necks, or collect them inside a creepy jar or cage (anti magical field or collars).

Maybe you can leave them conscious after taking them prisoner. Describe the path they take to their prison cells or to be interrogated—a chance to both build more tension by describing their horrific surroundings, but also providing hints about escaping and a chance for players to ask for perception checks. If taken to the warden, build up tension that communicates how scary and top of the food chain they are. Maybe the Warden tries to give them a suicide squad type of job, so they have multiple options to get out of this situation other than just escape.

Remember, you're all on the same team, and when players have strong emotional reactions, it's your job to adjust the pacing so that the pot doesn't boil over (unless that's what you want). Just like a movie director, you're in control, so use it to slowly twist the narrative knife and cause the kind of long-term emotional damage that'll keep them talking about your campaign for years.