The 1-0 success lifted the Clarets back into the top flight after a 33-year absence and has led to the highly-rated Coyle being linked with the vacant managerial post at Celtic.
Elliott said: "The main thing the manager brings is enthusiasm - it's infectious.
"He thinks deeply about the game, but then he just loves football. He still plays in reserve games and you can see how much joy he gets just being involved.
"Our football reflects how much we enjoy playing for him."