A 2-2 draw at the Stadium of Light left Wanderers still languishing inside the bottom three, but level on points with 17th-placed QPR, who play Chelsea at Stamford Bridge on Sunday.
They entertain Tottenham on Wednesday night and then West Brom next weekend before travelling to Stoke on the final day of the campaign, and Coyle is confident they can ease themselves over the line.
He said: "I am very confident - I always have been because I know what we have as a group and I know how hard we are working behind the scenes to implement bits and pieces we want at our football club.
"But within that, we realise that short-term, we have to make sure that we stay in the Barclays Premier League so then all the hard work we are putting in comes to a fruition.
"We will decide what happens to Bolton Wanderers. It's in our own hands to go and do that.
"We have taken 14 points from the last 24 - it probably should have been 16 on today's showing - so we know we are on a good run of form."
Bolton were indebted to the endearing quality of captain Kevin Davies, who was a January target for Black Cats boss Martin O'Neill.
The 35-year-old scored both of his side's goals, handing them a 26th-minute lead with a crisp volley and then snatching a point 20 minutes from time with a close-range header.
In the meantime, Nicklas Bendtner had levelled when he expertly controlled Jack Colback's pass and slid the ball past Adam Bogdan for his eighth goal of the campaign.
The Black Cats eased ahead 10 minute after the restart when James McClean curled an unstoppable free-kick over Bogdan and into the roof of the net, but Davies denied the home side a first victory in six attempts in the league with a powerful header from Martin Petrov's cross.
Had it not been for Gordon, who blocked an 87th-minute shot from substitute Ivan Klasnic, Bolton might have emerged with all the points.
Coyle said of Davies' contribution: "He was terrific. Kevin Davies out-with being a wonderful player, he's a terrific leader for our football club and a captain.
"He's that committed to the club that there was a period earlier in the season when he was trying to play through little knocks.
"I said to him at the time, 'Listen, you are better served now coming out of that and getting yourself fresh because we are going to need it', and that's proved to be the case.
"He has come roaring back in the last couple of months showing the form that had him in the England team last year, and that's what we need in the last three games.
"He is so conscientious, he is in there annoyed with himself because he gave the free-kick away that led to them going 2-1 in front, and that's the type of heart and everything that you need in this particular area of the league that we are in.
"Kevin Davies has got a huge role to play between now and the end of the season."
O'Neill was understandably disappointed after seeing victory snatched from his grasp, but admitted it was an illustration of the work which still needs to be done.
He said: "It would obviously have been great for us to win because at least for this evening, we would actually have gone into eighth position in the league.
"But I am not sure that we are an eighth-in-the-table team, that's the point. We are where we are.
"It was frustrating not to win the game today [Saturday]. I am disappointed, of course, but I said here a couple of weeks ago that we have work to do. That's not a problem."