The defender seemed to be in pain while holding his ankle after a collision in the first half against Liverpool but carried on playing after several minutes of treatment.
Coady went on to have a superb afternoon, despite the 1-0 loss, and Lage has revealed he has been dealing with a recent injury issue.
“In the last month he has been struggling with a problem in his ankle,” he said.
“That’s the spirit he has. Me, my staff and the medical department are working with him and we talk and every time he wants to be in the game. It is one of those problems we can manage and he can still play.”
Coady also made a wonderful block on the line to deny Diogo Jota after Jose Sa had wandered out of his goal and missed the ball.
And Lage is delighted with what his skipper is offering on the field.
“I think he’s improving with the team,” he added.
“It’s very good that people understand how Coady is important for us. The way we are defending, him, Max and Saiss are doing very well.
“He is an important guy because we start the game from the back. They are doing a fantastic job.
“That situation when Jose came out and missed the ball and I just saw Coady putting his body on the line and that’s what I want.
“If the younger guys can see the older guys giving their body for the moment, they also need to give everything for our team.
“I am very happy with my players and I say that since the first day.
“They come every day with the ambition to play the way we want to play and they come with that mentality.
“Against Liverpool, and Coady as our captain, helped me in that situation to create that culture and spirit. We want to continue to work in that.”