Coady has been in superb form for a number of months now, prompting many fans and pundits to say he is in the best purple patch of his Wolves career.
The centre-back notched his second goal of the season with an instinctive finish in the 3-1 victory over Southampton and Lage believes it is a just reward for his skipper.
“He deserved it (the goal),” Lage said.
“Coady is a leader, he is our captain and I am very proud to work with him.
“Also the other guys because they work very hard and they are playing with my ideas.
“They want to play my ideas and they are there every day to try to understand.
“This week it was very hard to prepare this game because Southampton usually play 4-4-2 but sometimes against a line of five they change and in the last games they have changed to a line of five.
“We prepared both systems and we did very well. That’s why this victory is so important for us and also for him (Coady) because he is doing very, very well.”
Wolves had to endure a tough start to the game as they survived a number of Southampton chances.
Jose Sa superbly kept them in it, too, but Lage says his side deserved the win on the balance of the game.
“It was a good result against a strong team,” he added.
“The first half was very hard, especially the first 15 minutes.
“We know how they play, they come with high pressure every time to put the other team under pressure.
“In the first 10 minutes they had a lot of situations and a lot of corners. We didn’t find the right tempo in the right spaces to play.
“But every time we fight and then in the second half it was our best 45 minutes. I think in that period we were better than them.
“In the end, when you look at what we did, it was a good result for us.”
Meanwhile, Coady hopes that Adama Traore will stay with Wolves this month.
The winger, who has 18 months left on is his contract, has been the subject of transfer speculation for some time.
He scored his first goal of the season on Saturday and Coady hopes the Spaniard will comit his future to the club.
Coady said: “It is an amazing feeling and a massive result for us.
“It would have been a crime if I had missed, I nearly did.
“But I was more happy for Adama than I was for me, I will be honest with you.
“He deserves everything he gets and he deserved that goal.
“He is the hardest worker I have ever met in my life.
“He is an incredible person and I am over the moon for him.
“It was important he got it and hopefully he can build on that now for us.
“I don’t think there is any footballer like him in the world with his power and aggression and how quick he is.
“It is an absolute pleasure to have him here.
“We just hope he stays with us as long as possible.”