The Clarets now face Sheffield United at Wembley in a £60 million promotion playoff and Coyle said: "They have been magnificent from day one. You have seen that again tonight.
"We rode our luck in the first half. Reading showed they have Premier League players in their ranks, but we stood up to what they had to offer."
He added: "I always believed we were capable of being in the mix at the top of the league. The lads have shown strength of character, desire and hunger.
"I am delighted with the application we showed at the end. They are a unified bunch and it is not easy to leave some of them out. They all deserve a starting place.
"Each and every one of them gives me everything on a daily basis and I can't ask for any more than that."