United lost the final in 2018 after only conceding 1 goal before the final.
City lost the final in 2013 after only conceding 1 goal before the final.
United lost the final in 2005 after only conceding 1 goal before the final.
Liverpool lost in the final in 1988 after only conceding 1 goal before the final.
That’s the best I can do to answer your question, they are all from 1980 onwards so nobody has done what we’ve done and lost from 1980 onwards. There are many years where I can’t find the info on goals conceded on the road to the final without proper going into everyone’s season-by-season records.
It should be noted that City broke a few records in the Champions League in 2020-21 before losing the final to Chelsea:
Longest winning run in UEFA competitions: 7
9th December 2020 – 4th May 2021
(record by an English team)
Most wins in UEFA Champions League in a season: 11
2020-21 season
(record by an English team)
We won 11 of 12 games on the road to the 2021 CL final and the other was a draw, then lost the final.