It is a match vital for two sides desperate to stay in the top flight and, although Bolton are currently second-bottom of the table, a victory would lift them above their 15th-placed opponents.
Tensions will undoubtedly run high with Burnley fans angry at Coyle's desertion but Steinsson said the players were treating the game as any other and were keen just to do well for their new boss.
"It is a tragedy for them but that is just how football is," said the Iceland international, who scored his first FA Cup goal in Saturday's 2-0 fourth-round win over Sheffield United.
"He really wanted to come here. That is what we players see and feel.
"That gives us a boost because he wants to have this challenge with this group and he will take this team forward.
"The players have been buzzing around with the new manager and the positive attitude he and his staff brought with him."
The Coyle effect has already been felt at Bolton with two encouraging performances in defeats against Arsenal - including going 2-0 up at the Emirates Stadium before losing 4-2 - and that was in evidence again against the Blades.
After a turgid first half, the Scot highlighted a few key points at the interval and within three minutes Steinsson had put Bolton in front, shooting through goalkeeper Mark Bunn's legs from a narrow angle from Kevin Davies' pass.
Six minutes from the end substitute Johan Elmander produced almost a carbon-copy for the second, courtesy of the ever-improving Lee Chung-yong.
The win was Coyle's first since taking charge just over a fortnight ago.
"It is a relief for the manager and the players," added Steinsson, who insists the squad are well prepared for their relegation battle.
"It has been a good two weeks. There has been a lot of sharpness around the training ground.
"In the years I have been here we have been more of a direct team but we have shown in the last couple of weeks we can pass it around.
"If we go out there and play like we did yesterday and against Arsenal then the points will come and we'll get higher up the league.
"It won't happen overnight but if we continue like this we will secure our position.
"We have been here before, we have a couple of games in hand and we are confident in the things we can do.
"I'm looking forward to the coming weeks and months. I am really positive about the things happening here and I am really pleased to be playing for him (Coyle).
"Players are really enjoying their football again."
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