After Coyle's heroics in getting Burnley promoted to the Premier League before his departure to Bolton last week, Laws has a tough act to follow and his appointment has received a mixed response from the club's supporters.
However, the 48-year-old insists he is ready to prove to his worth to the Turf Moor faithful and show that he is the right man for the job.
"They (the Burnley board) believe they have made the right decision, and I do," Laws said.
"I'm sure with the supporters time will tell but all I'm asking of them is support your team as you have been, continue to do what you are doing and we will do everything in our power to get it right on the pitch.
"Owen has done a terrific job and rightly should be looked at through the eyes of the supporters as a legend.
"He has done something that many managers have tried and been unsuccessful. Credit where credit is due and I know that the fans will support that and say he has done a brilliant job.
"I'm sure there will be one or two reserved that will be looking and watching what happens. All I can say to them is that they will get my full commitment.
"I'll work every hour possible to make sure it happens at this football club.
"Time will tell and I hope I do. Every club I've been to I've had a great affinity with the supporters. I appreciate what they're about and I hope they see that."
Burnley became renowned under Coyle for their free-flowing football, an approach which has brought them a great deal of success but has also led to some heavy defeats on their travels this season.
With survival the priority for this campaign Laws acknowledged the Clarets' need to modify their strategy for away fixtures, but the new manager also stressed that the attacking style which has proved so popular with supporters would not be sacrificed.
"They do play expansive football and I have watched a few of the games," said Laws, whose first game at the helm will be a trip to Manchester United on Saturday.
"Each approach (for away games) has got to be different, there is no doubt about that - you are playing different teams and they have different approaches.
"I think we just have to look at that and tinker with it. There is not a great transformation in what we are trying to achieve here - we are not saying we are going to make wholesale changes or that we are going to change the style of play.
"I just think we can tinker with it and sometimes fresh ideas will help support the players and give them license to express themselves but maybe be a bit tighter away from home.
He added: "I like to play good football. There's good players here and they like to play football. It's a marriage made to work.
"I'm not going to be changing anything - there's no broken wheel here as far as I'm concerned. We'll add one or two bits but we want to tick over what Owen has done and just add a little bit more."
Laws said that every player at the club would be starting with a "clean slate" but admitted that he would have to assess his options quickly with almost half of the January transfer window having already passed.
"They (the current players) all want to play and all want to be part of it so I'm going to have a good look at that," Laws said.
"Having said that, I've got to work quickly and maybe made some pretty hard decisions pretty quickly, because when we strengthen, we've only got a short window."
Laws has been joined on the new coaching staff by Russ Wilcox, his assistant at Wednesday, and veteran Clarets midfielder Graham Alexander.
The club have also been linked with a move for Plymouth Argyle assistant manager John Carver, although Burnley would not confirm whether an approach had been made.
Burnley chairman Barry Kilby insisted Laws was always the club's first choice for the job.
Kilby said: "He has been the first choice out of some really excellent candidates. We have been really impressed by his demeanour and his passion for Burnley Football Club.
"He stands out. Being an ex-player and having an affection for us helped as well.
"I think his record at Sheffield Wednesday, when you look at the budget Brian had to work with, was excellent as well.
"Burnley, being the size we are, we have to work within our budgets. It is an exact fit for us."
Kilby admitted the club did speak to O'Driscoll but insists compensation was not an issue because a decision was made to appoint Laws.
He added: "It wasn't compensation, there were no stumbling blocks. We had several excellent candidates, of which Sean was one.
"It was simply Brian came out in front of the pack and is the one we have chosen to give this job to and I'm sure we'll have success."
Laws has a tough task in following Coyle, who guided the Clarets back to the top flight after a 33-year absence.
Yet the former Republic of Ireland striker was also a surprise appointment just over two years ago and Kilby hopes the club's judgement pays off again.
He said: "They're all gambles. You never really know until you get out on that pitch. There are parallels from when we took Owen on and let's hope it is successful."
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