You are correct when you say that, "St John tells us that there were many things Jesus did/said which were not recorded in the scriptures."
If fact, those that demand proof from scriptures, the Bible, are in fact wrong. How do I know this? St Paul tells us clearly that 'Solara Scriptura', belief in the Bible's written word is wrong. Believing only in the written word of the Bible is wrong. Read St Paul's message (2 Thessalonians 2:15), So then, brothers and sisters, stand firm and hold fast to the teachings we passed on to you, whether by word of mouth or by letter.
This is a clear teaching of St Paul that 'Sola Scriptura' is not a true doctrine. No where does the Bible claim that Scripture alone is the authoritative word of God.
If I were to ask you what is the pillar and foundation of God's word, would you answer, the Bible or the Church? Many would answer 'The bible alonel', Well, you'd be wrong. What does the Bible say is the Pillar and foundation of the Church? In fact, the Bible itself tells us that the Bible is not the pillar and foundation of the truth, instead it is God's Church. (1 Timothe 3:15) So those who ask you, where is this in the bible disregard the truth of Paul's teaching.