Jurgen Klopp's side moved onto 97 points from 38 games thanks to Sadio Mane's double, but Manchester City's 4-1 win at Brighton and Hove Albion means the Reds' 29-year wait for the top-flight crown goes on.
Hope was kindled among the home fans when news of City going behind arrived shortly after Mane turned home, but once Pep Guardiola's side moved ahead before half-time, Liverpool appeared resigned to their disappointment.
Senegal star Mane got his 22nd of a superb league campaign with nine minutes to go, but celebrations were largely muted in the Merseyside sunshine.
FULL-TIME Liverpool 2-0 Wolves— Premier League (@premierleague) May 12, 2019
It's not enough to claim the title - but a strong performance from Liverpool and two strikes from Sadio Mane ends an incredible season for the hosts with 97 points #PL #LIVWOL pic.twitter.com/oSFhnz7enG
Liverpool dominated the early possession but created little until 17 minutes in, when Mane converted Trent Alexander-Arnold's low cross.
The noise around Anfield suddenly cranked up when news of Brighton's opening goal came through, but the atmosphere was dampened when City overturned their deficit before the break, shortly after Rui Patricio parried a fierce strike from Andrew Robertson.
Wolves were beginning to show some endeavour, too, and only the crossbar denied them a leveller before half-time when Matt Doherty beat Alisson with a fine first-time strike.
Divock Origi - the hero against Barcelona this week - missed a good chance on the turn, but Wolves continued to threaten against a tired-looking Liverpool side and Jota was denied by Alisson after a clever dummy from Raul Jimenez.
Mane moved joint-top of the goal-scoring standings - alongside team-mate Mohamed Salah and Arsenal's Pierre-Emerick Aubameyang - with a clever header from Alexander-Arnold's cross, although he should have been flagged for offside, before Virgil van Dijk hit the crossbar late on as Liverpool finished an outstanding season with a flourish.
12 - Trent Alexander-Arnold has provided 12 assists in the Premier League in 2018-19: the most by a defender in a single campaign in the competition. Adventure. pic.twitter.com/0bnDFqLBXg— OptaJoe (@OptaJoe) May 12, 2019
What does it mean? Liverpool treading new ground - but league glory still eludes them
Only Guardiola's City have ever amassed more points in a Premier League season than Liverpool in 2018-19. They lost only once - at the Etihad Stadium - and have gone unbeaten at home for consecutive seasons for the first time since 1980.
And yet, it was still not enough. The Reds could end up champions of Europe, but conquering England is still just out of reach.
As for Wolves, 57 points and a seventh-place finish is a commendable return under Nuno Espirito Santo.
Matip a man-mountain
While all the plaudits this season have gone Van Dijk's way, Joel Matip has quietly been enjoying probably his best spell for the club. He was supreme against Raul Jimenez and Diogo Jota here.
Jimenez misses out on Kop dream
Jimenez spoke before the game about wanting to score at Anfield, but he barely had a sniff of a chance and was mostly marshalled too easily by the centre-backs in red.
Wolves will look to build on a sterling campaign back in the top flight. They have been the best team outside the top six all season and could perhaps look to break into that group over the coming year.