B767-300 technician reported not downgrading the aircraft after replacing the Thrust Management Computer.

Narrative

On the night of Day 0; it was brought to my attention by the crew that all indications pertaining to the thrust management system were not displaying as they should. They informed me that the indications were there when they started their pre flight; but a few minutes prior to load complete they were no longer there. I had them create a logbook entry as we started our troubleshooting process. Logbook entry was as the following Thrust management computer TMSP (Thrust Mode Select Panel) - INOP blank. As we came to the conclusion that the thrust management computer needed to be removed and replaced; the aircraft had been load complete for some time. I ordered the part; removed and replaced it; and I ran the installation test all according to the AMM (Aircraft Maintenance Manual) 22-XX-XX/XXX. Everything tested correctly and I signed it off. Leaving an hour or so late.On this night; we also had been assigned to five aircrafts. Also tasked with training a new AMT (Aircraft Maintenance Technician). There was a lot of pressure to be asked by the company to catch; oil; handle any inbound write ups; complete paperwork; answer/explain any questions from the new AMT; and have all five aircrafts depart on time. Even from the start of the night without any aircrafts in our gateway; we already had a stressful and unclear mindset trying to come up with the perfect execution. During the discovery of the issue with the thrust management computer we had been notified that another aircraft that we were assigned to had an issue with a lower cargo door closing. Its hard to be in multiple places at once; so we were under a lot more stress/pressure now due to this aircraft being late for departure already and adding another aircraft that needed to have an issue resolved with a departure time coming up soon also. As we waited for the new thrust management computer to arrive; that is when we started jumping back and forth between aircrafts trying to use our time as wisely as possible. That aircraft also ended up leaving an hour late. All in all; I fully take ownership in my mistake of not downgrading the aircraft as it should have been. I do think that the issue could have been avoided if we hadn't been assigned to five aircraft. That is way too much for the company to ask for in an 8 hour work period. Juggling between the 2 aircrafts with active write ups and having to kick other planes is when I over looked and did not perform my double checks; seeing that the aircraft needed to be downgraded. To prevent this from happening again and being able to perform our duties accurately and with a clear mind requires more staffing. The shortage of staffing and the pressure and stress from upper management to accomplish task quickly is to be the biggest concern for me. I also think that the technology we have should have prevented me from signing off something that I am not qualified to do. If we had that technology even in the busy state of mind that I was in; it would have reminded me that I was unable to complete that task without this specific qualification. That is why we make sure that our certifications in our software program are accurate and up to date.