A solitary goal from Ronan Hale in the first-half would prove to be the match winner, and despite admitting his side were lucky in the first 15 minutes of the contest, Boyle felt they could have found the back of the net themselves.
Their best chance saw Jordan Mooney being denied by a superb save from Reds stopper David Odumosu.
However, the Reds held firm in the second-half and should have killed the game off when Ben Wilson hit the woodwork, as well as Joe Gormley and Stephen Mallon who both had efforts thwarted by Tom Murphy.
"We were probably lucky not to be three goals down inside the first 15 or 20 minutes,” Boyle said.
"I thought we had managed that storm but then we conceded a poor goal from our point of view.
"However, we grew into the game and if it was 3-3 at half-time, I don’t think anyone would have had any complaints.
"We carved out some good opportunities against a good side but ultimately we didn’t score.
"We are producing good performances but we aren’t getting the results which matter to show for them.”
The result keeps City in 11th place and Boyle remarked that a clear split between the top six and bottom six is there for all to see.
"I think there is a definite split,” he added.
"To be fair to Loughgall, they have had some big results and have spent time in the top six so far this season.
"However, you can see the quality the top six teams have and they are able to get results when not playing at their best.
"We were very good for 45 minutes against Linfield and got nothing from the game, we should have taken something from our home game against Larne, and we were narrowly beaten on Saturday against a good Cliftonville side.
“The top six teams are definitely better at dictating results but it is what it is and we have to keep working hard.”