In their last appearance at the MCG before finals, Fremantle led for 70 minutes of the match, but were overwhelmed late by the never-say-die Demons.
Leading by 15 points following Nathan O'Driscoll's major 11 minutes into the final term, the Dockers conceded four of the last five goals to suffer just their third defeat of the season.
Fremantle will still almost certainly be minor premiers, guaranteeing them two home finals at Optus Stadium.
But if they are to break through and win their maiden premiership 31 years after entering the AFL, the Dockers will have to get it done at the MCG on grand final day.
"We didn't handle some moments, clearly," Longmuir said after Saturday's loss.
"I don't know whether that was the ground or the crowd; we hadn't been in that situation for a while, so we'll review it.
"But we've got no fears here.
"Come back and try to improve our footy."
Fremantle opted to rest captain Alex Pearce for the trip east to ensure he is ready to go for the finals.
But Longmuir conceded Pearce's absence properly cost the Dockers the tight game, with Melbourne taking several crucial marks inside-50 in the last quarter.
"We thought we'd manage him for the travel, an away trip before the back end of the season," Longmuir said of Pearce.
"We might have done that if we were fifth on the ladder, sixth on the ladder.
"I don't think today's down to we're getting comfortable or we've just dropped back a little bit," added Longmuir.
"We played a really good side who's been beaten once here, and we're in front with eight minutes to go.
"We didn't quite handle the last period of the game long enough.
"We had some players down on form today, not at their best, so we'll need them to get going a little bit."
The Dockers will warm up for the finals against Adelaide (home) and Carlton (away).
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