Those defeats meant their final Group G game against Tunisia was little more than a dead rubber, with neither side harbouring hopes of making the last 16.
A first-half own goal from Meriah put Panama into the lead in a World Cup game for the first time in their history, and also set a more general landmark.
It was the nation's second goal of the tournament, meaning that all of the 32 participating countries in Russia have hit the net at least twice over the course of this first round.
That had never previously happened at a finals, even back in Uruguay in 1930's inaugural World Cup when just 13 teams were involved.
Curiously, Panama have netted the same amount of goals as holders Germany, who also managed just two in an awful campaign.
Denmark, meanwhile, are the only team to advance having scored two goals in their three matches, while Group C colleagues France also have the worst attack of any group winner, with three in their campaign so far.
At the other end Uruguay stand out as the meanest team by far in defence, alone holding the distinction of having kept a clean sheet in each of their first round encounters.