Lebanon captain Robbie Farah argued with the on-field referee over the call, saying his side should not have been penalised because Moujalli took great care not to run into any defenders as he made his way through the line.
"He hasn't impeded anybody," Farah argued.
"Tough, tough call," one commentator added. "There wasn't much of an obstruction.
"There's nothing in that."
Speaking after the match, Moses left nobody in any doubt he believes the men in charge got the call wrong.
"I'm pretty heartbroken right now. The boys dug deep and stayed in the game for 80 minutes but a few calls didn't go our way," Moses said.
"There was a try opportunity there and we had those calls not go our way for the whole tournament.
"It's just heartbreaking to see how hard the boys worked and to be pulled up with some calls that weren't right. We'll hold our heads high but we're knocked out now.
"To see how hard the boys worked and to be pulled up in that manner is pretty heartbreaking."
Farah was just as devastated as he came to grips with the knowledge he wouldn't be lacing the boots up again in this tournament.
"Real gutted," Farah said. "It was a game that was there to be won.
"We came here with a lot of belief, a lot of confidence we could get the job done and we knew they were within reaching distance in the last 10-15 minutes and that we were a chance but we just couldn't get that try to get us in front.
"I'm so proud of the boys. We're a team made up of mostly part-timers and to play England and Australia and then back it up against Tonga over here in New Zealand is a top effort."
The early indications were this clash would be a try-fest as both sides crossed in the opening 10 minutes. David Fusitu'a found space on the right wing before releasing back inside for Tui Lolohea who was following in support to register the opener, then Doueihi struck back almost immediately for Lebanon.
Farah showed some trademark sleight of hand at first receiver before linking up with Moses 20m out from Tonga's tryline. Moses passed to fullback Anthony Layoun who then gave an early ball to Doueihi, the centre stepping back inside off his left foot to break the line and score a four-pointer.
Quick hands and a spectacular one-handed put-down in the corner from Fusitu'a gave the Tongans a 10-6 lead and Will Hopoate made it 16-6 when he was the beneficiary of an Andrew Fifita offload on the left edge.
Lebanon then started to turn it on, playing some enterprising footy that captivated fans. Moses broke through the defence 10 minutes before halftime then launched a bomb into the air, only for his kick to clock Tongan forward Jason Taumalolo in the head.
The ball took some freakish bounces to make its way into the in-goal and Moses chased, he and Fusitu'a diving desperately to ground the ball. Both missed the Steeden and the ball continued to bobble in the danger area, allowing James Elias to come into the picture and force the ball for a try.
An Abbas Miski try from a grubber followed by a Tongan penalty goal made it 24-16.
Lebanon's four-pointer in the 69th minute was the highlight of the match. The Cedars played hot potato with the football, going forwards and backwards, right to left then back to the right again as they miraculously kept the ball alive for what seemed like an eternity before finally crossing for a try.
The ball went through 14 sets of hands before the play ended with Miski scoring on the right wing to make it 24-22.
Tonga made several errors as it looked to be crumbling under the pressure of keeping a resilient Lebanon at bay, but it held on in the end to finish with a two-point win and progress to the semi-finals.
