The Scot's arrival from Burnley in January appeared to have the desired effect as Wanderers moved out of the bottom three to stand 13th in mid-March, eight points clear of the drop zone.
But successive defeats against Everton, Manchester United and Aston Villa - with Chelsea at Stamford Bridge to come - have again raised fears of relegation.
Although there are still other clubs who are more likely to go down, Coyle knows he has to ensure his side at least maintain the five-point gap between them and third-bottom Burnley, especially as their final two games of the season are against Tottenham and Birmingham.
"Sometimes from a fan's perspective you win a couple of games and the world is your oyster or you've lost and it is all gloom and doom," said Coyle.
"You have to give balance to it. You have to make sure your players are ready to give their best each and every time.
"Our focus is from one game to another, we don't take it in blocks of three or four.
"If we were Barcelona and had lost to Everton away, Manchester United and Aston Villa then we might be disappointed but I think you have to put into context who you are playing.
"We accept we have had some tough games but the Aston Villa game could have gone either way, against Manchester United we were terrific for 70-odd minutes or so and Everton we were very comfortable until we had a man sent off.
"People forget seven games ago we were in the bottom three and we went about our business, won games, played well and took ourselves out of that dangerous position.
"Then we came into a tough run of games. We now have to stabilise and win the points to stay in the league.
"The table changes from week to week. All we can do is concentrate on our own games to make sure we stay in the Premier League and get those points as soon as possible."
The chances of taking points off Chelsea at Stamford Bridge still appear slim - Manchester United manager Sir Alex Ferguson described it as an "easy game" for Chelsea" - but Coyle remains optimistic.
"Every man and his dog will have written us off already," said the Bolton manager. "In football everyone has an opinion but we have to go out and disprove that theory.
"These games always throw up the chance for the underdogs to win and I've done that a few times in my career.
"We came into the club in January, haven't spent a penny and lifted the team out of the bottom three.
"With five games to go we will do everything we can to get enough points to ensure that we are safe.
"It is in our own hands and we have to do everything we can to get the points."
Source: Team Talk
Source: Team Talk