Southampton spent six of the nine seasons in the Premier League, from 2012/13 to 2017/18, and three before that outside it. Without City they finish fifth twice, on 60 points both times. Neither is enough for the top four.
In 2014/15 fourth place takes 64 points, four more than Southampton’s. In 2015/16 Manchester United take it on 62, two more.
The rest is a trade. Southampton played City 12 times in the league, won two, drew two and took 8 points. Take City out and all 8 come off, and the wins cost the most. The 3–1 in February 2013 was Mauricio Pochettino’s first win as their manager. In 2012/13 and 2016/17 the points off City outweigh City’s place, and Southampton finish lower than they really did: 15th, not 14th, then 9th, not 8th.
Every other season moves them up. Twice it is only the free place, the one every club below City gets. In 2014/15 and 2017/18 the climb goes one place further.