City haven't played Aston Villa since the 1974-75 season, when both clubs were in (old) Division Two. City beat Villa the first time they played that year, December 28, 1974, at Ninian Park but that won't help here as it was well before Villa won the big cup in 1982.
Prior to Saturday, City's last win over Nottingham Forest came on April 23, 1977 (the 40th anniversary of that big win at Wembley), also in (old) Division Two. Forest hadn't yet won a European Cup at that time, of course, so no help there either.
Neither Liverpool or Man United will work either. City haven't even played the Reds since December 12, 1959 (years before their first cup in 1977) and haven't beaten the Red Devils since November 26, 1960 (years before their first, in 1968). So no help in either of those two cases.
I'd have to say, then, that Saturday's win was City's first over a former winner of the European Cup since the 1-0 win over Real Madrid at Ninian Park during the 1970-71 Cup Winner's Cup competition.