Hey-- not a Liverpool fan, and this won't be a particularly long post, but I just developed a model that projects out the remaining fixtures of the Premier League, and I figured this would be as good a place as any to share some of that.
Long story short: Liverpool's chances of placing top 5 dwindled from 17% to 7%.
Before the game, my model had Liverpool at 1% to finish 3rd, 4% for 4th, 12% for 5th, 31% for 6th and 7th each, 14% for 8th, 5% for 9th, 2% for 10th and under 1% for 11th-14th combined.
Now, Liverpool's at 1% to finish 4th, 6% for 5th, 22% for 6th, 29% for 7th, 22% for 8th, 13% for 9th, 5% for 10th, 1% for 11th and 1% for 12th-14th combined.
Some brief notes about my methodology:
I create skill ratings for each team through an iterative process-- essentially, I give every team an initial skill of 1, then see how predictions of the form (HomeTeamSkill+HomeAdvantage-GuestTeamSkill) perform against the actual results, see how much each team over- or underperformed their initial skill, add that to the original estimate, and then repeat that a couple of times until the estimate becomes stable.
For instance, Liverpool is estimated to have a skill of 1.44, which is basically identical to the Spurs-- ManU is at 2.13, Aston Villa at 0.06. That also means that ManU would be favored by (2.13-1.44) goals over Liverpool on a neutral field, and that Liverpool would be favored by (1.44-0.06) goals over Villa on a neutral field. Home field advantage is about a third of a goal. Liverpool's rating is functionally tied with Tottenham's for fifth-highest in the League, which means that they really underperformed their skill so far this season. It's also the reason for why my model thinks Liverpool still has a better shot at pulling off a Top-5 finish than Swansea or West Brom do.
From these point estimates and the standard errors they have when the predictions are fitted to the actual results it's easy to simulate the rest of the season, add up the results, and look at the final standings over a couple thousand simulations.