Albrighton was a key member of Craig Shakespeare's team at the start of the season but he was overlooked by Puel after he arrived at the King Power Stadium.
The winger was left out by Puel for his first two games in charge, with Riyad Mahrez and Demarai Gray getting the nod.
However, Puel has used all three of them in his team in recent weeks and the former Aston Villa man insists he is happy to push himself in order to play.
He told the Leicester Mercury: "I am used to it and a few lads in there are used to having people chasing them, people who aren’t in the team trying to get your shirt. That is football these days.
"We have got some fantastic players here and you need competition to keep pushing yourself but it is difficult when someone is chasing you down, someone like Riyad who has proven to the world what a good player he is, and Demarai, who is a great prospect for the future.
"It is always going to be difficult to compete with them but I feel I bring something different to those two in my own way."