The 22-year-old tapped in Raheem Sterling’s 75th minute cross to seal the first win of the Pochettino era.
After earning his first win as Chelsea manager, Pochettino was full of praise for Chelsea’s no9 at Stamford Bridge.
He said: “We knew Nicolas Jackson’s quality when we signed him, we saw that before. It is not that we ask him to run and press the ball, he is quality in the way he recovers the ball, but he also can finish.”
“It is only a matter of time, once he settles into the Premier League, he will show it more. Nicolas Jackson has top quality. I have no doubt that he can become one of the greatest strikers in the Premier League.”
Sterling was the man of the match after scoring the opening goal through a placed finish after dribbling in and out of several Luton defenders.
He added a second by turning in Malo Gusto’s cross before earning a standing ovation when substituted in extra time.
Pochettino revealed exactly how he has got the best from the England international, who struggled last season, adding: “I need to hope Raheem will be happy [about my answer].
“Our first conversation with all of the players, and Raheem, I love to ask the position they love to play, how they feel, how they see themselves in front of the mirror.
“It is not the position, it is the animation and how the team is going to link in between.
“To find the best position for the dynamic of the game we are playing in an offensive situation to try to provide the best platform and position and place and link to the player that can appear their best quality.
“That is why the process is important, trying to work to create all these links and the way that we want to play and animation and to know each other we need time.
“When you are in a team in the process that we are, it is a matter of time.”