Their 2-2 draw at Stoke City wasn't enough to beat the drop.
Coyle said: "We'll take our medicine, I will as a manager, but we certainly believe, regardless of the personnel we had missing and the trials and tribulations of the season, that we still had enough quality, and we do.
"Our young players will continue to get better, that's the transition we've been making this year, but we wanted to do that off the platform of being in the Barclays Premier League.
"My feelings are not for me, they're for our wonderful support and the chairman and the owner. It's a wonderful club.
"The players are very quiet and sombre, it's not a feeling I've become accustomed to as a manager but it's happened and it's about how you react to adversity. We will regroup and we'll look to bounce back straight away."