Gary Cahill and Daniel Sturridge scored in each half to record a routine win which puts the Trotters back in the hunt for a European place.
Coyle said: "It was a terrific performance and a hard-fought victory. We knew we would have to be at our best against Everton and we were. There were so many positives to take from the game.
"We had to withstand some spells of pressure because of the quality the opposition have, but I felt we looked a threat all day.
"We've had a little dip over Christmas and new year when we were down on numbers, sometimes having only 15 players.
"We managed to address that in the window and it is always great when the players you bring in play well."