The Rabs boss says his side were punished for not making the most of their first-half superiority at New Tinto Park.
A scrappy Evan Lowdon goal just before the break was enough to give Benburb the victory, much to Maxwell’s disappointment.
He said: “We played really well for the first 35 minutes. We dominated but never scored.
“We then lost the scrappiest goal right on half-time when the ball hit off our defender and rolled over the line to give them a goal out of nothing when we were the better team.
“In the second half, we were into a howling wind in 80 degrees on the astro and we just didn’t play.
“I-m bitterly disappointed we never took at least a draw out of the game, and I probably would have been disappointed with that
“We’ve lost another tight game because we just don’t score when we’re on top and it’s come back to bite us.
“There were a lot of positives, and we worked really hard, but you need to win games.
“We played well for 35 minutes. We were really solid and defended well, but after we lost a terrible goal, they had something to defend in the second half.
“Even though we didn't play well in the second half football-wise, we still had one cleared off the line and their keeper had a great save.
“We put a lot of effort in but without any reward unfortunately."
“To give Benburb credit, they battled and took an ugly 1-0 win and got the three points, which is what it’s all about.”
Rabs have little time to dwell on their disappointment, however, with a tough home double-header coming up against Auchinleck Talbot tonight and Clydebank on Saturday.
“We’ve told them the disappointment doesn’t last long because the champions roll into town,” said Maxwell.
“They're a top side, and they’ll battle just as hard as Benburb but with more quality about them.
“It’s another learning curve and we’re not expected to take anything from the game, but with a young team you never know.”