Werenski, 19, was injured with 6:45 left in the second period when he was struck under his shield by a shot from Penguins forward Phil Kessel. Werenski immediately went down, was bleeding from his face, and went to the locker room.
He returned for the third period with a full face shield, but his eye had swollen so much he couldn't see and was unable to play in overtime.
The Penguins won 5-4 to take a 3-0 lead in the best-of-7 series. Game 4 is at Nationwide Arena on Tuesday (7:30 p.m. ET; CNBC, SN360, TVA Sports 2, FS-O, ROOT).
"It makes you sick just because you see him try to come back out and his eye's swollen up between the third and overtime and you know he wants to come back out, and what guy comes back out in that situation?" Blue Jackets captain Nick Foligno said. "I said to him, 'I'm proud to be your teammate.'
"He's a kid who exemplifies what we're trying to build here, and it's pretty impressive from a young guy. There's lots of respect for that kid around the room, always has been. He's such a big part of this team and it's hard not to have him out there."
Werenski set a Blue Jackets record for points by a rookie with 47 (11 goals, 36 assists) and was first in NHL scoring among rookie defensemen
He scored his first NHL postseason goal Sunday playing on the top defense pair with Seth Jones. Werenski averaged 23:29 minutes in three playoff games and was minus-2.
"I've said it all along, as we get more and more questions about that guy and what type of pro he is, he is on a fast-track path to be one of the mainstays in this league," Tortorella said.
That Werenski returned after the injury proved to his teammates how tough he is.
"It's pretty incredible what he did and after seeing him today, how his eye has closed up," defenseman David Savard said. "He's a tough kid. He showed a lot of resiliency."
Tortorella did not say who would replace Werenski in the lineup, but it likely will be Kyle Quincey or rookie Markus Nutivaara. Neither has played in the series.