Sebastian Larsson curled home a consolation free-kick in the fourth minute of injury-time but it could not prevent the Clarets extending their 100% home record to four matches.
"Having won the three games at home and then coming off the back of the heavy defeat at Tottenham last week and not having an enjoyable week a lot of people will have perceived us to win this game," said Coyle.
"Sometimes they are the games you trip up on but we didn't. We stuck to our guns.
"Birmingham are one of the teams who are going to be in our group. We are not getting carried away, we know exactly where we are and where we expect to be.
"That is why, for me, it was the biggest result of the season. If we can pick up points from the teams round about us that will serve us well for the duration.
"The result against United was fantastic but I really believed we had to answer up after last week to retain our 100% record and hopefully it sends out a message to people that Turf Moor is not an easy place to come."
Coyle was reluctant to single out players but admitted he was pleased for Fletcher with some people starting to question whether he was worth the £3million Burnley paid Hibernian in the summer.
"Steven is a talented player but he was a little bit frustrated having had a perfectly good goal disallowed at Tottenham last week," added the Clarets boss.
"He has already shown his pedigree and has scored goals in the Carling Cup. He's 22 years of age and I think he will get better.
"I don't necessarily need my strikers scoring goals to contribute to the game because of what I ask them to do in terms of how they play for the team.
"David Nugent has not scored today but his work-rate was terrific and that is what I am after.
"Fletcher comes into that category. He works his socks off looking to improve himself individually and if he is doing that it helps the team.
"I am loathe to talk about individuals because that was a team performance today.
"I was disappointed we gave away the cheap free-kick but, having said that, it was good execution from Larsson."