"I'm not a quitter. It's not in my nature to consider quitting," said the 30-year-old pop star.
"We are just starting on a long road and I know I can help make the path smoother for some of the celebs."
Following Saturday night's show, viewers logged on to message boards to debate her debut appearance.
While some were still lamenting the loss of 66-year-old choreographer Arlene Phillips, whose departure caused a furore, Alesha promised she would bring new experience to the panel because of her time on the show as a contestant.
"My job is not to replace Arlene. My job is to provide a perspective that was maybe missing before," she said.
"And that is the understanding of the performance aspects and just how tough it is to perform to the standards the viewers expect."
In response to the criticism she faced over her comments to the contestants, the Let's get excited singer says: "You can't please all the people all the time. You don't get much time to decide what to say."
Apart from Alesha's debut, the other big talking point of the night was Lynda Bellingham's twirl on the floor.
The press are already hailing her as this year's John Sergeant after she won over the audience despite a less than nimble-footed performance.
"I'm here to entertain and that is what I'm going to do," the 61-year-old Loose Women presenter told viewers.