The Chelsea midfielder has started four out of Norwich's five matches in the Premier League this season.
The Canaries have gone winless in those games, and Gilmour knows he must continue to improve in difficult circumstances.
"I knew it was going to be difficult. It's my first season and I'm at a newly promoted club," Gilmour told the Evening News.
"There's more to come as I adjust but I feel happy and settled here. I love playing under the boss and I'm just waiting for that first win and the points to come on the board.
"Most of my game is on the ball but I've learned a lot so far. I can run a lot and I like to put a tackle in. I'm working my hardest off the ball and every week is a new challenge.
"I'm a young player and this is my first full season in the Premier League so I'm really enjoying that side of it and trying to get the game time whilst learning under the boss."
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