The 19-year-old was handed his first start for the Ayrshire club in last week's Clydesdale Bank Premier League game against Hibernian. The match was abandoned after supporter James Haswell collapsed in the Rugby Park stands with a suspected heart attack and, sadly, later died in hospital.
The youngster hopes Shiels will keep faith with the same group of players when they travel to Dundee this weekend.
He said: "There are a few games to go and I would like to start those games but I just have to do what I can do and hopefully impress the manager. Hopefully the manager keeps the same team because I thought the team did well. We will just have to wait and see how things go."
On the tragic circumstances surrounding the last match, Davidson added: "The game was stopped and we were all told to go inside.
"I looked over and saw the fan being treated. It was quite hard for the players to take. The guy was actually from where I stay and I'd see him at a lot at the games."
Life-long Killie fan Davidson believes the combination of a productive loan spell at Airdrie, and the guidance of some of his boyhood heroes, means he is now better prepared to stake a claim.
He said: "It's the club I've supported since I was a wee boy so it was brilliant to get a game in front of the fans.
"I looked up to players like Garry Hay and James Fowler when I was younger. In training, they speak to you a lot and they help you on and off the pitch.
"I was at Airdrie for a month and did well there. I was going to go back out but it didn't happen so I've been trying to push myself to get into the team here. I felt as though I became stronger because I was playing with physical players in the First Division and that helped me quite a bit."