"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, who swapped Burnley for Bolton just over a fortnight ago.
"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."
Coyle dismissed reports of an alleged training ground bust-up between goalkeeper Jussi Jaaskelainen and Phil Hughes, brought in from Burnley as goalkeeping coach to work alongside Jaaskelainen's long-time mentor Fred Barber.
"I've been to the training ground every day and I've not seen anything," said the Wanderers boss.
"I can assure you the lads have worked their socks off. Football being football there are always going to be things thrown up, but if it happened I was not aware of it.
"They (Hughes and Barber) work together with the five goalkeepers we have at the club - it is not rocket science, it is very plain and simple."
United boss Kevin Blackwell felt his side had matched their hosts but had failed to take their chances, with Henri Camara missing a one-on-one with Jaaskelainen midway through the first half.
"I thought there was nothing in the teams. They were two sloppy goals, make no bones about it, and straight after half-time it was disappointing," he said.
"Really you would have been hard pressed to work out which was the Premier League side today.
"When you concede goals as early as that we had to chase the game and it disrupted us a little bit.
"If we had taken our chances in the first half the game could have been dead and buried.
"I thought we played well enough to get something out of the game."