I can find only one allusion in the poem. The title and the last two lines:
The old Lie: Dulce et decorum est
Pro patria mori.
The "old Lie" is that "it is sweet and fitting to die for your country," which is an allusion to Odes iii.2.13 by the Roman poet Horace.
How sweet and fitting it is to die for your native land:
Death pursues the man who flees,
spares not the hamstrings or cowardly backs
Of battle-shy youths.
Latin was a part of most secondary school curricula before World War I, and this expression would have been well known. Owens points out how horrific war is and that it is not "sweet and fitting."