Davis impressed on debut in defeat to Blackburn Rovers.
"It was a great occasion for me and hopefully the first of many," he told the Express & Star.
"It's a lot faster and a lot more physical. The tempo was very high. It's a big step up. It was different to League One and the SPL (Scottish Premier League) but I thought I did alright.
"Hopefully I can impose myself in training because there's a big game on Sunday.
"I have to train my hardest and give TC (boss Terry Connor) a bit of thought towards having me involved against Manchester United."