There is no Salvation Except through Faith in the Qur'an
Allah says: O Muhammad, say,
يَـأَهْلَ الْكِتَـبِ لَسْتُمْ عَلَى شَىْءٍ
(O People of the Scripture! You have nothing...) meaning no real religion until you adhere to and implement the Tawrah and the Injil. That is, until you believe in all the Books that you have that Allah revealed to the Prophets. These Books command following Muhammad and believing in his prophecy, all the while adhering to his Law. Before, we explained Allah's statement,
وَلَيَزِيدَنَّ كَثِيراً مِّنْهُم مَّآ أُنزِلَ إِلَيْكَ مِن رَّبِّكَ طُغْيَـناً وَكُفْراً
(Verily, the revelation that has come to you from your Lord makes many of them increase in rebellion and disbelief.)
فَلاَ تَأْسَ عَلَى الْقَوْمِ الْكَـفِرِينَ
(So do not grieve for the people who disbelieve), Do not be sad or taken aback by their disbelief. Allah said next,
إِنَّ الَّذِينَ ءَامَنُواْ
(Surely, those who believe) referring to Muslims,
وَالَّذِينَ هَادُواْ
(those who are the Jews) who were entrusted with the Tawrah,
وَالصَّـبِئُونَ
(and the Sabians. ..) a sect from the Christians and Magians who did not follow any particular religion, as Mujahid stated. As for the Christians, they are known and were entrusted with the Injil. The meaning here is that if each of these groups believed in Allah and the Hereafter, which is the Day of Judgement and Reckoning, and performed good actions, which to be so, must conform to Muhammad's ﷺ Law, after Muhammad ﷺ was sent to all mankind and the Jinns. If any of these groups held these beliefs, then they shall have no fear of what will come or sadness regarding what they lost, nor will grief ever affect them. We discussed a similar Ayah before in Surat Al-Baqarah 2:62.
Tafsir Ibn Kathir (abridged, English).