Coyle has challenged his side to repeat the second-half performance they produced in Tuesday night's 2-1 win at Aston Villa for the remainder of the campaign.
Bolton lie in 18th place but are now only one point behind QPR and Wigan and still have a game in hand after chalking up a fourth victory in the last seven games.
Coyle said: "We've got 13 points from the last 21 and have been in good form. Our rivals have been winning as well but we know what we have got to do.
"We have got to make sure we produce performances like the second half against Villa to remain in the Premier League.
"We have been decimated by injuries but are still in there fighting and our destiny is in our own hands.
"The lads stood up again to be counted away from home in a hostile atmosphere and came from behind for the second time in three days to get something from the game [after Saturday's 1-1 draw against Swansea]."
Goals from Martin Petrov (penalty) and David Ngog sealed victory for Bolton after Stephen Warnock had put Villa in front.
Coyle added: "People keep writing my lads off, and I say 'carry on doing it' because I know what we have got in that dressing room.
"We have got four cup finals left but we always knew we were masters of our own destiny, which is good.
"There's still a lot of hard work to be done but there's so much character in this squad."
Coyle acknowledged the part played by veteran striker Kevin Davies in Bolton's survival fight in recent weeks.
Davies came off the bench at half-time against Villa and caused constant problems to their defence during the second 45 minutes.
"In the last couple of months, Kevin has been in terrific form," Coyle said.
"He scored at Tottenham and Wolves, was outstanding at Newcastle, started against Swansea and did well, and was outstanding when he came on against Villa.
"You always know what Kevin is going to bring to the party.
"I knew if we had Kevin on the pitch alongside with David Ngog, we'd have a better goal threat than the first half and that is exactly what happened."