After Hwang Hee-chan's early goal, Wolves were hanging on for all three points as the game ticked into the 94th minute.
The slightest of touches between Nelson Semedo and Joe Gelhardt saw the former crash to the floor and win a penalty that was converted by Rodrigo to rescue a point.
And Lage believes his side were unlucky to have the decision go against them, while he also criticised his side's defending in allowing Gelhardt to get into that position in the first place.
"We were in control of the game in the last minutes," Lage said.
"In the same way we won the last game we dropped two points here and I think all of the situations were very soft.
"The way we defended that situation, because the player received the ball with his back turned to our goal. He had a chance to turn and enter between our defenders.
"From my point of view, and I didn't see the situation on TV, but I think it was very soft for him to go on the floor.
"This is football. I don't want to discuss the decision.
"What I want is to try and understand. We did well when we were defending and controlled everything.
"But in the same way it's very hard to play against them. They press and have a lot of men to follow our players, like Hwang, Adama and Raul.
"It wasn't easy for us to have more time with the ball. That's my concern from the 90 minutes.
"We did well in defence and the strategy was there because they didn't have too many chances and we controlled everything, especially the inside game.
"But with the ball we didn't look after it."
After scoring in the first 10 minutes Wolves sat deep for the majority of the game and soaked up the Leeds pressure.
They were also struggling to make the ball stick up front with Hwang, Raul Jimenez and Adama Traore – with the latter in particular looking isolated and frustrated.
And Lage has revealed the Leeds press was causing them problems as they failed to keep hold of the ball in attacking areas.
When asked if he was concerned at how deep his team sat, Lage added: "Leeds know how to do a lot of things. One thing is the way we tried to press and we had a strategy to press higher, especially from our right side.
"When it came to that side we wanted to press with Adama, Raul and Semedo and press high.
"You want to give confidence to the players and in the break we spoke about needing to press and if you look, our decision was to continue to give fresh men in the front to try and press.
"I changed Adama for Daniel to continue to press and have more time on the ball. I was trying to change Hwang for Trincao when Rayan asked for the substitution.
"We didn't have the ball and two or three times it came forward and we lost the ball. The emotional side then comes to you to be solid and compact.
"We lost the ball and continued the same position. It was very hard for us because we wanted to start from the defenders and midfielders and put the ball in front between the lines, and every time Raul, Adama and Hwang were man to man and they didn't have the chances to create or keep the ball.
"It was more about that, not having the ball, than keeping the (deep) position."