Yep, I was 14 at the time and travelled up on the train with my schoolmates as all the supporter buses were full.
They closed the gates just after me and my mates got in about 10 minutes before kick off, I never heard of any Saints fans who never made it in, but there was a few thousand Sheep supporters locked out. ( the joys of the old pay at the gate days ).
As you pointed out I think we would have won the league with wins in the last 4 games,
From a fading memory think we Lost 2-0 to Aberdeen, lost 2-0 to an already relegated Hibs, drew 0-0 with Celtic and beat Rangers 4-1.