The Brazilian netted his 110th Liverpool goal a minute from time in his final home game for the club.
But a point did little for the Reds’ faint chances of hunting down Newcastle and Manchester United for a top-four finish as they both now need just one point form their remaining two games to guarantee Champions League football.
A point also aids Villa’s chances of a return to Europe for the first time since 2010.
Unai Emery’s move one point ahead of Tottenham in seventh with victory over Brighton in their final game next weekend good enough to secure at least Europa Conference League football next season.
A seven-game winning streak had kept Liverpool’s chances of reaching the Champions League alive.
But that run had masked a desperately poor campaign from Jurgen Klopp‘s men, who came close to an unprecedented quadruple of trophies last season.
This time there will likely not even be the consolation of a top-four finish for a trophyless season, which could have an impact Klopp’s budget in the transfer market for a summer rebuild.
It could have been worse for the hosts as Villa missed a first-half penalty taken by Ollie Watkins.
The England international won the spot-kick as he outpaced Ibrahima Konate and was brought down by the Frenchman.
But Watkins’ poor penalty record continued as he slotted wide to miss for the fifth time in nine attempts in his career.
Villa, did not have to wait long for the opener as Jacob Ramsey’s cool finish at the far post steered home Douglas Luiz’s cross on 27 minutes.
Klopp was serving the first of a two-match touchline ban after questioning the integrity of referee Paul Tierney following his side’s win over Tottenham last month.
The German’s presence was missed in a lacklustre performance but Klopp might have found himself in further trouble had he been on the touchline as two major decisions went against his side.
Firstly, Tyrone Mings survived a VAR check for a red card for a high challenge that left stud marks on Cody Gakpo’s chest.
Gakpo then had the ball in the net on the hour mark after a goalmouth scramble.
But after another lengthy VAR review, referee John Brooks decided Virgil van Dijk’s role in the build up from an offside position was in the same phase of play and the goal was ruled out.
Firmino was introduced from the bench 20 minutes from time and all that was lacking from a fairytale finish was a Liverpool winner after he steered home Mohamed Salah’s cross.
But Villa held out for over 10 minutes of stoppage time to leave Newcastle and Manchester United with the champagne on ice.
Newcastle can clinch Champions League football for the first time in 20 years when they host Leicester on Monday.
United have two home games against Chelsea and Fulham to get the job done in Erik ten Hag’s first season in charge.
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