Dyche oversaw the club's remarkable rise to the top tier last time out, when Burnley finished second in the Championship having been tipped to struggle when the campaign began.
They have held their own this term despite some tricky fixtures, yet Dyche knows Burnley must improve upon a points haul of two from four games - with Saturday's visit of Sunderland seemingly representing a good opportunity.
He told Sky Sports News: "It's a stern challenge. The Premier League is arguably the best league in the world, but we think we are applying ourselves in the correct fashion and are looking for that first win.
"The general performances have been good, but we want to improve that cutting edge. We know we are a work in progress.
"We have to get points on the board. Defensively, we've been solid but we have to get goals. At the moment, we're not far away."
This year represents Dyche's first taste of the top flight as he continues a superb start to life in management.
The former Watford boss is relishing every moment, adding: "It is great for me as a young manager. My learning curve has been quick and steep."
