The former Old Trafford trainee raced onto a pass from fellow substitute Jay Rodriguez and lofted the ball over visiting goalkeeper Keiren Westwood.
It was salvation for Burnley and while Tuesday night's 1-1 draw at Turf Moor was not enough to lift them into the Championship play-off zone, a fitting reward for their efforts over the 90 minutes.
"We deserved three points and were by far and away the best team tonight," said Coyle.
"The lads showed tremendous belief and character to keep going and the goal from Chris Eagles was a quality finish.
"He's been out of the starting line-up for a few games recently due to a chest infection.
"But when he came on he showed the tenacity and drive that we saw earlier in the season and that bodes well for the run-in.
"The only negative was losing a goal but otherwise we dominated the game and I'm proud of the lads."
For Coventry, going nowhere in the Championship but dangerous on their day as Burnley's neighbours Blackburn almost discovered to their cost in the FA Cup last weekend, it was so nearly the perfect smash-and-grab raid.
Best, wearing a protective mask to cover his face as he recovers from a fractured cheekbone, headed home shortly before half-time after Burnley defender Stephen Jordan allowed Jordan Henderson to hook the ball back to the far post.
Coyle added: "We shot ourselves in the foot and we are disappointed with the goal we lost.
"But that goal aside, they only had three long-range shots all night.
"The goalkeeper (Keiren Westwood) was outstanding for them and that's why he's so highly rated.
"Defensively Coventry were terrific but we really should have taken a bigger percentage of our chances.
"However, I was always believing we that there was goals in us. But we should have had a few more.
"Many teams would have felt sorry for themselves but this group of players don't know that.
"They kept going right until to the end to get a positive result."
Coventry boss Chris Coleman accused his side of failing to maintain their impressive first-half showing after the break.
He said: "I think before the game we would have been happy with a point at Burnley.
"They are going for the play-offs and had just beaten Wolves.
"In the first half we were not in any danger but we sat back for the second 45 minutes and I'm disappointed with that approach.
"Sooner or later you are going to concede and in the end we buckled."