It is not right to state that there is no reference to Shanta, daughter of Maharaja Dasharatha and adopted daughter of Anga Raja Romapada in Valmiki Ramayana. In the Tenth Sarga of Balakanda verses 28 to 31 reads as follows:
तत्र चनीयमने तु विप्रे तस्मिन्महात्मनि |
ववर्ष सहसा देवो जगत्प्रह्लादायंस्तदा || २८ ||
वर्षेणैवागतं विप्रं विषयं स्वं नराधिपः |
प्रत्युद्गम्य मुनिं प्रीतः शिरसा च महीं गतः || २९ ||
अर्घ्यं च प्रददौ तस्मै नियतः सुसमाहितः |
वब्रे प्रसादं विप्रेन्द्रान्मा विप्रं मन्युराविशेत् || ३० ||
अन्तःपुरं प्रविश्यास्मै कन्यां दत्त्वा यथाविधि |
शान्तां शान्तेन मनसा राजा हर्षमवाप सः || ३१ ||
On the Muni reaching the city gates, Lord Indra sent showers to the kingdom of Romapada, which gladdened everyone's heart. The rains betokened the arrive of the Rishi, so thinking Romapada went to receive the Rishi with all humility and welcomed him by offering the high seat, water for abulations and fruits and water for consumption. He also prayed for a boon that his (Rishyashringa's) father Maharishi Vibhandaka should not be angry with the king. Romapada then took the Rishi Kumar to the women's quarters offered his daughter Shanta of the calm demanaour in marriage performing the rituals as prescribed.
In the eleventh sarga Dasharatha's minister Sumanta further recounts what he has heard from the Sanat Kumaras of Dasharatha's friendship with Romapada and the request for Rishi Rishyashringa to come and preside over the sacrifice for begetting heirs.
So there is mention of the story of Rishi Rishyashringa and Shanta in Valmiki Ramayana, but yes there is no mention she is Dasharatha's daughter. That reference as you rightly said is detailed in Srimad Bhagavad Mahapurana.