Flight Instructor with student reported they were informed after landing they had a near miss in the traffic pattern with an aircraft on final approach.

Narrative

I was in the pattern with a student at ZZZ with four other aircraft. The active Runway was XX. On our first approach to land; I instructed the student to demonstrate a go-around. On our departure leg; I was aware of a citation jet landing behind us; and a Skyhawk extending its left downwind for the citation traffic. The pattern was standard until the downwind. On downwind and abeam the Runway XX threshold the Skyhawk was still on short final; so I instructed my student to postpone configuring for landing until abeam the aircraft. Once abeam the aircraft on final; we began our descent; turned base; then final and landed from a standard pattern with standard radio calls for each turn. Upon landing; it was communicated to me that there was an additional aircraft [Aircraft Y] that was on an extended final for Runway XX that I did not realize was there. Neither my student nor I noted a radio communication from the conflicting aircraft indicating their position on final; however; it is possible the call was missed by me or stepped on. I looked for traffic towards the north and west before turning base and did not see traffic. I was dividing my attention between traffic awareness and instructing my student on his traffic pattern and landing. I believe the aircraft was below our position and to our north when we turned base. On final; I still did not see any traffic; but it is likely the conflicting aircraft was directly below us. The aircraft executed a 360 turn towards the north away from our position before re-entering the final approach. In addition to not seeing the traffic; the traffic did not appear on ADS-B. Going forward; I will prevent this situation from happening by utilizing a more thorough visual scan for traffic. I will also be sure to maintain better situational awareness of traffic in the pattern at ZZZ by prioritizing an accurate mental model of the traffic pattern before executing any turns to base and final.