On the contrary, Indrajit actually fired the Brahmāstra on Rāma and Lakṣmaṇa in the main war of Rāmāyaṇa.
When both Rāma and Lakṣmaṇa are lying unconscious in the battlefield, this is what Vibhīṣaṇa says:
तस्मै तु दत्तं परमास्त्रमेतत् | त्स्वयम्भुवा ब्राह्मममोघवेगम् |
तन्मानयन्तौ यदि राजपुत्रौ | निपातितौ को अत्र विषादकालः || ६-७४-४
4. etat = this; braahmam paramaastram = excellent missile presided over by Brahma the creator amoghaviiryam = with never-failing
strength; dattam = was given; svayambhuvaa = by Brahma; tasmai = to
Indrajit; maanayantau = honouring; tat = it; rajaputrau = the two
princes; nipaatitau = were made to fall down; yudhi = in battle; kaH =
what is the use of; viShaada kaalaH = a time for despondency; atra =
This excellent missile, presided over by Brahma the creator, with
never-failing strength, was given to Indrajit by Brahma. Honouring it,
Rama and Lakshmana the princes fell down in battle. This not a time
for despondency here.
Before Indrajit makes his first appearance in the main war, this is what he does:
सोऽस्त्रमाहारयामास ब्राह्ममस्त्रविदां वरः || ६-७३-२७
धनुश्चात्मरथं चैव सर्वं तत्राभ्यमन्त्रयत् |
Indrajit, who was skilled in the use of mystic missiles, invoked the missile presided over by Brahma and charged it on his bow, chariot and all.
Before falling to the ground, Rāma suspects Indrajit has somehow employed the brahmāstra and says the following to Lakṣmaṇa:
मन्ये स्वयम्भूर्भगवानचिन्त्यो |
यस्यैतदस्त्रं प्रभवश् च योऽस्य|
मया सहाव्यग्रमनाः सहस्व || ६-७३-७०
I think the self-born Brahma who is the source of the universe is inconceivable and this missile is presided over by him. O wise one! Remaining undistracted in mind, you bear along with me today the hail of arrows here.