Thanks for calming the nerves
A bit on the maths:
Let's compare what the different teams need to get to a given threshold, say 71 points, which seems to me the lowest number you'd consider to mean safe passage into the top 4.
We would need 12 points over our last 8 games. For instance, if we beat Wolves, Chelsea and Fulham at home and Bournemouth away, we could afford to lose our remaining four games (Spurs A, Villa H, Brighton A, West Ham A). We need 1.50 pts per game, and have 1.90 per game so far this season. In Other words, we can afford to significantly drop our results compared to the season as a whole. This clearly means we have every opportunity to finish well above the threshold needed for top 4, if we finish the season reasonably well. 75 seems more than realistic.
Newcastle would need 15 points in their last 8 games. They could afford, for example, to lose at home to Arsenal and draw away to Spurs, Leeds and Chelsea if they win their remainder (a very winnable sequence of Everton A, Southampton H, Leicester H, Brighton H). This would require them to perform on the same level as they have so far this season (1.88 ppg, 1.90 for the season so far). This makes for a very credible 3rd place challenge - it's not that hard to imagine them pipping us by 3 points in the remaining games.
Spurs can only drop 3 more points in their remaining 7 games to get to 71 - for example, losing away to Newcastle and winning all of the rest (including us, and away to Liverpool and Villa). That would mean 2.57 pts per game, compared to which they have taken 1.70 across this season. In other words, they'd have to go on an absolute tear. Can't see many signs of that. In my opinion, their top 4 aspirations effectively died with the home loss to Bournemouth.
Brighton would need 22 points in their remaining 9 games. That would allow them one loss and one draw, the rest must be won. With City, Arsenal, United, Newcastle and Villa remaining on the menu, that would be quite a feat. They're at 1.7 pts per game this season, getting to 71 would take 2.44 pts per game for the rest of the season. They'll be gunning for something like 63-65 points, which should suffice for 6th place and Europa League qualification, and that won't be easy either.
Villa would have to win all of their remaining seven games to get to 71. That would be twice their season ppg of 1.50, and would include beating all of United, Newcastle, Liverpool, Spurs and Brighton. That's not going to happen.
Then there's Liverpool, who could get to 71 but need to win all of their remaining nine games to do so. That seems very unlikely unless they suddenly hit a kind of form they haven't shown all season, but their run-in is by some distance the easiest of all the teams mentioned here. Their only big opponents left are Spurs and Villa, both at home. Two more points dropped, and they're toast, as far as CL goes.