The head coach has kept the same starting XI in all five of his Premier League games so far this season.
But good performances from a handful of players in the cup – most notably Willy Boly, Leander Dendoncker, Daniel Podence and Hwang Hee-chan – has led to some supporters calling for changes.
Lage has always come across as a friendly character who enjoys speaking to his players and supporters, as well as engaging amicably with the media.
But he has now revealed he chooses not to have ‘personal relationships’ with his players so that he can easily make tough decisions if needed.
When asked if any of his players are undroppable, he said: “No. I want competition and every time is an opportunity to give me something.
“They are doing what they are doing in games, and in training. Players are coming, Daniel coming from a long period of injury and Hwang is coming from some questions to solve without a good pre-season.
“That’s why we analyse everything to look at what the players give me and what we need for the next game. Then take the best decision.
“That’s why I don’t have a personal relationship with anyone. I want to be free to take the best decisions for me and the club.”
After scoring against Spurs in the Carabao Cup on Wednesday, Podence could be in line for a start at Southampton on Sunday.
When asked if the winger will get his Premier League chance soon, Lage said: “They know they need to continue to work hard.
“Some players did well and some players did not do well. In the game they did what they’re doing in training so it was not a surprise for me what guys like Daniel did in the game, because he’s doing well in training.
“It’s a question of what you give every day for us. Every moment we are in this process.
“That’s why it’s a long season and I try to choose the best decisions for the games. Sometimes, one player comes on and scores one goal but it doesn’t mean he needs to play from the start. He can also do the same job to help us.
“It’s also about the best strategy to play against the other team, so that’s why our job is about decisions.
“We have four wingers and they can give us different solutions. The thing is to choose the best two for each moment.
“I’ve known Daniel since he was little, I played against him when he was 10-years-old. I’ve played against him lots of times at under-10s, under-15s and under-17s.
“I know what he did at Sporting, Olympiacos and here. I know him very well and the things he can do for us and to help us in our game.”