Even if we'd won against Birmingham on the last day of the 1974-5 season we would still not have got into europe. Can't remember the reason - Darren or Silent may be able to help.
The story is this...
The UEFA cup was the successor to the Inter Cities Fairs Cup which was founded in 1955 as a tournament for cities (not clubs) that held trade fairs. As it was cities that entered, if there was more than one professional club in the city, sometimes a collective XI from all the said clubs would be selected (A London XI was runner up in the first tournament) and sometimes one club was selected to "represent" the city.
Originally, entries did not go on league placings and were chosen by the Fairs Cup Committe. Famously, in 1962 when we finished 5th in the First Division and Wednesday had finished 6th, the Fairs Cup Committee chose Wednesday to represent Sheffield (even though the FA had nominated United).
As the 60's wore on, teams did end up getting selected on the basis of league placings and collective city XI's no longer took part. However, despite it being something of an anomoly, the one club one city rule remained.
The UEFA cup replaced the Fairs Cup in 1971 and the qualification for English teams was as follows: the League Cup winners got a place (unless they were not a First Division team) as did the three highest place finishers in the First Division from 2nd downward (unless the League Cup winners were a non First Division team, when it would be 4). However, the one city one club rule still remained, so if two clubs from the same city would otherwise have qualified, the League Cup winners or the higher placed one only got an entry. Thus in 1973, Arsenal finished runners up in the League and Spurs won the League Cup, thus Spurs got London's place and Arsenal got nowt.
That rule was still in place in 1975. As we went into that last game at Birmingham, Villa had a place as they had won the League Cup (they were a 2nd Division team but had got promoted), Liverpool had one as runners up and Ipswich as the 3rd place finishers. Everton were 4th but, as the rules were then, could not qualify as Liverpool FC had the city of Liverpool's place.
Stoke were in 5th and would thus get the last place, unless United won at Birmingham when they would overhaul them. As we know, we only got a draw, so it looked like Stoke had qualified. However, Everton protested at this and, during the summer, UEFA recognised that the rule was a bit daft and cancelled it, letting Everton in and kicking Stoke out.
And that's how it happened guys and gals....