Gretar Steinsson and Johan Elmander scored for Bolton to secure Coyle his first win.
“When you come into any job you want to hit the ground running and get a win as early as you can and it was nice to get it today,” said Coyle.
“Accepted my first two games were against Arsenal, who have tremendous quality, but I thought we did enough in those two games to win football matches and we did that today.
“I felt the first half was quite even and I just told the lads at half-time to pass and move the ball a bit more and take care of it rather than be one-dimensional in our play.
“We did that and scored two very good goals and could have had a few others.
“I’m delighted to take the win, a clean sheet and a lot of positives in terms of the goal threat we had, particularly in the second half.”