The 16-year-old A-level student was eliminated from the BBC competition after Team Odyssey lost a task involving hair products.
The teams were tasked with creating a brand for a new hair product, with Maria Doran's Team Platinum naming their range Strexy.
Lord Sugar said of the product: "That makes me Strumpy - strong and grumpy."
Turning to Odyssey team leader Andrew Tindall's product Chameleon, Lord Sugar said it was contradictory to their concept of "standing out".
Explaining which team won the challenge, he told the candidates: "I consulted with the advertising agency and I don't think we were far apart in our thinking.
"Andrew - your advert was confusing, you tried to be too clever and, I'm afraid, we all concluded that it's backfired. Maria - yours does what it says on the tin, and you shoved that tin right in the face of the viewer. For that reason - you've won."
Team Platinum were rewarded with visiting Labrinth while he recorded a new track, while Team Odyssey were sent to the Losers' Café.
Lord Sugar asked Andrew what he thought of Navdeep's involvement in the task, with the 16-year-old replying: "To be honest it did feel like Nav was playing out a strategy, she wasn't really getting the team to win. She thought it was a clever move by disagreeing with the concept to start with."
A surprised Navdeep responded: "I think you're thinking way too much into it!"
Taking about their advertising, Lord Sugar said: "This advert to me looked like a government warning - beware of thieves stealing hair gel in dressing rooms."
Andrew decided to bring Navdeep and Steven Cole back to the boardroom. Steven stated his shock at being asked back, with Andrew explaining: "I just didn't think he was anything special."
However, Andrew insisted that Navdeep should be fired for this particular task, saying: "She claims she's this all-rounder and, from what I've seen, she's really not."
Lord Sugar gave his final verdict, saying: "Steven - I do like your spirit, I like your openness and honesty. Today, I'm going to let you go back to the house.
"Navdeep - my concern and my instinctive feeling is, yes you are highly intelligent, but I still have these feelings about whether you have got this business nuance about you.
"Andrew - five times loser. If I had to put this information into a computer and it was done on statistics and not gut feeling, you know what the answer would be.
"Although I'm not a computer, I have to say it's very difficult for me not to act upon that. It is regretful, it is with sincere regret, that I'm going to say that, Navdeep - you're fired."
Navdeep said of her experience on the show: "To get six weeks into it shows that I've done something amazing and I'm really proud of myself. I thought I was an amateur when I began and I've managed to beat out a lot of people. I do think that the future's going to be incredibly good for me."