Having lost 6-0 in the previous meeting between the clubs at Larne - and 6-2 in the club’s previous league meeting at Carrick - Glenavon finished down by 3-1 in the weekend Lurgan meeting.
Harry Flowers and Albert Watson each steered home headers off corner-kicks by Martin Donnelly before the break.
Stephen Murray’s second-half penalty kick cut the gap to 2-1 but hopes of a Glenavon fightback finished in defeat when Johnny McMurray grabbed the game’s final goal.
“Every wee rub of the green seems to be going against us at the minute,” said Hamilton. “We lost Andrew Doyle and Andrew Mitchell to injury at half-time, having earlier lost James Singleton on the morning of the match with a neck problem.
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“We cannot seem to get a settled side together, we’ve had to make changes for Carrick and again today, so unable to get consistency.
“It’s difficult to get that 90-minute performance when chopping and changing, especially the back four as such a vital area.
“To be fair, today the boys responded in a really positive way to the half-time substitutions.
“Jordan Jenkins came on and made an impact, Daniel Larmour did really well and I felt we deserved a draw off the second half.
“But at the other end Larne proved clinical, when on top in games you must make it count to stand any chance.
“When making so many changes each week it’s really difficult to have a back four familiar with each other.
“But we still should do better - especially conceding six away to Carrick.
“But one of the positives was how we came out in the second half to stay in the game until the sucker-punch on the break.
“They started really well and it took us time to get to grips with Larne but then we did but conceded off two set-piece plays.
“We conceded two goals so similar from set-pieces by not getting tight enough to our men.
“Most of Larne’s first-half efforts came from outside the box and we would expect Jonny Tuffey to deal with those moments.
“In the second half I felt we played some really good stuff and had chances to equalise, at least.
“Even just before they scored the third we had an opportunity on the edge of the box, didn’t take it and Larne broke away.
“Now we’ve more out for Tuesday against Carrick at home, that’s part of football and we go in searching for a reaction and three points.”