Wanderers pulled themselves out of the bottom three with an impressive 3-1 home victory over Liverpool in their last league outing and are now 17th in the table.
However, Coyle knows plenty can happen in the remaining 16 games and, after a run of only two defeats in their last nine games in all competitions, he wants to maintain that momentum.
"I think there is always a stigma involved in being in those (relegation) positions," Coyle said ahead of Wednesday's home game with Arsenal.
"But the important time to be out of the bottom three is after the last game of the season, ask any manager and they will tell you that.
"We have now given ourselves a foundation and a platform to continue the good work that we have done in the last month and a half or so, but to do that we need to be at our best.
"The Premier League is unforgiving and you have to be at your very best every time you cross that white line."
Like Bolton, Arsenal have had major injury problems to contend with this season, with news emerging last week that key midfielder Jack Wilshere - who spent a loan spell with the Trotters in 2010 - had suffered a setback in his attempt to recover from an ankle injury sustained in the summer.
In his absence the Gunners, who are fifth at the moment, have been out of the title race and are facing a battle to finish in the top four.
Manager Arsene Wenger has been frequently criticised and the London outfit travel to the Reebok Stadium - where they were beaten 2-1 in April - having lost their last three league games in a row.
However, although there is certainly cause for optimism on Wanderers' part, Coyle pointed to Arsenal's dramatic comeback from 2-0 down in their 3-2 FA Cup fourth-round victory over Aston Villa on Sunday as clear evidence that Wenger's side cannot be underestimated.
"I think we all recognise it, because we are in the best league in the world, within that comes global scrutiny and decisions get questioned," Coyle said.
"The bottom line is that Arsenal are very fortunate to have one of the best managers in world football.
"Expectations are raised because they have won honours and haven't been in amongst them again, but for me it is an outstanding club with a fantastic manager and some truly world-class players.
"We are going to have to be at our very best, that is for sure, but if we are, we know that we can win the game.
"We won the same fixture last year and we have to get to that level again.
"You only have to look at Sunday. Arsenal found themselves 2-0 down, but then their second-half performance with their quality, speed of passing, pace, movement, counter-attacking...this is an elite club with aspirations of winning the Champions League, of making sure they qualify for it again via the Premier League, of winning the FA Cup.
"They also have been decimated by injuries to key players. When you are missing the calibre of player of Jack Wilshere, who is not only an integral part of the Arsenal squad but also the England squad now, it is going to take its toll from time to time.
"But they keep on staying in the mix and that is all credit to Arsene and the players he has at his disposal."
