However, the Glasgow-born boss got the victory he craved thanks to Chung-Yong Lee's fifth goal of the season.
In the process, Bolton moved out of the relegation zone and dropped Burnley into it for the first time since winning promotion under Coyle.
Not only that, the club chalked up a clean sheet for the first time this season in the Premier League.
Iceland international Steinsson said: "It was really important for us to win this game for him (Coyle) and maybe justify his decision to come here.
"It is also for us and now it is the time to look up as we are out of the relegation places.
"We did really well and defended solidly. I felt really confident we were not going to concede.
"A clean sheet is something we should be proud of and something we should have been doing more frequently this season.
"In my mind, we have got the strongest team since I have been here, so we have the players to go higher up the table."
Coyle is pleased with South Korea star Lee's progress following his arrival from FC Seoul in the summer.
With Vladimir Weiss and Stuart Holden also on board until the end of the season, Coyle is keen to change the dynamic of the side.
He said: "We are trying to bring in exciting players. There is no doubt that Weiss can play and Lee continues to excite.
"Weiss likes to get at full-backs and get crosses in while Holden has great energy and desire. He wants to show he can play in the best league in the world, so he is a young man with a point to prove.
"There is plenty to work with. It won't happen overnight, I don't have a magic wand and it takes hard work on the training ground.
"But the players are responding to the stuff we have implemented. However, this is just a start and we have to continue that progress."
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