It's been said 732 times before, but
Up until 1974-5, qualification for the UEFA Cup had a one city one club rule - only one club could qualify from the same City. In England, there were 4 places - one for the League Cup winners and then the 2nd, 3rd and 4th teams in the League. However if 2 teams from the same city qualified only the highest got a place and the place went down to the next highest place team.
In 74-5, before the Birmingham game, placings were as follows:
1. Derby
2. Liverpool
3. Ipswich
4. Everton
5. Stoke
6. Sheffield U
We could only overtake Stoke if we won at Birmingham.
Villa had won the League Cup so, they qualified for the UEFA Cup and Liverpool and Ipswich were also in. Everton could not qualify as Liverpool were in. Hence the last place would go to the 5th place team - United or Stoke. As United failed to win at Birmingham, Stoke were in.
Or so we thought. In the summer of 75 UEFA abolished the one club one city rule so Everton were in after all and Stoke not. Hence United would not have qualified even if they had won at Birmingham and finished 5th.