Making matters worse, the faltering Sharks risk losing Tom Hazelton (hip-drop tackle) and Mawene Hiroti (rib injury) with the finals less than a fortnight away.
The usually mild-mannered Fitzgibbon punched a computer monitor in his coach's box as frustrations from a poor month bubbled over in Sunday's second half at CommBank Stadium.
"When everyone's livelihood's on the line and you're down 7-1 on penalties, yeah, you get frustrated. But I shouldn't have done it, to be fair," he said.
Cronulla sat a win clear inside the top four after round 22, but losses to St George Illawarra, Canberra and the Eels have now consigned them to finish the regular season either fifth or sixth, missing the double chance in the finals.
Fitzgibbon said the Sharks' recent struggles had "definitely" been mental, as the perennial contenders scramble to make the most of their potential at the business end.
"Let's be blunt, we're waiting for the semis and we're not playing what's in front of us," Fitzgibbon said.
"We're uptight because we're playing teams that have got nothing to lose and we've got everything on the line and we don't want to get it wrong.
"It creates an energy that we've got to address and we've been trying to, but we just haven't gotten over the top of that."
The Sharks will now be left to defy 30 years of history in pursuit of a second premiership. No team has won the grand final from lower than fourth since 1995.
Sunday's result confirms Penrith, the Warriors, Dolphins and Sydney Roosters as the top four for 2026, though the exact order will not be determined until next weekend.
In the absence of the injured Braydon Trindall, halves duo Nicho Hynes and Niwhai Puru struggled to spark the Sharks, who were playing catch-up from the opening minute.
Apa Twidle scored the Eels' first try before Cronulla had even touched the ball, after Kitione Kautoga burst through a feeble Hynes tackle and streaked away.
"That sort of set the tone for us and we were able to execute opportunities that we had after that, so that was very pleasing," said Eels coach Jason Ryles.
The Eels went 85 metres for their second try after Brian Kelly picked off Puru's pass.
Still unsigned beyond 2026, five-eighth Ronald Volkman came up with one of the great individual tries this season, dummying through Hynes then stepping past Will Kennedy on a 55-metre tear.
Trailing 26-8 at the break, the Sharks threatened to make a contest of it as Blayke Brailey crossed from a Twidle knock-on and Sione Katoa completed his double.
But their hopes of a comeback were quashed when Hazelton went to the sin bin for his hip-drop tackle on Volkman in the final 10 minutes.
Tallyn Da Silva crossed to seal the Eels' win minutes later, before nabbing a second try in the final minute.
"I thought we got out-enthused and outperformed. When you're chasing your backside like that, the discipline gets on top of you. We were never really in it," Fitzgibbon said.
Hazelton's record means he is no guarantee to play again this season.
If he receives a grade-two charge and takes an early guilty plea, the prop will miss next week as well as two finals games, if the Sharks progress that far.
Hiroti could join him on the sidelines after leaving the field injured just after Katoa's first try.
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