Sadio Mane scored a double but Liverpool's 2-0 victory over Wolves was in vain as they fell just a point short of Manchester City after a pulsating Premier League title race.
City's 4-1 win at Brighton means they retain the title ahead of Liverpool, whose 29-year wait for a top-flight title goes on despite a record tally of 97 points for a second-place side.
Needing a win and for City to drop points at Brighton, Liverpool took the lead through Mane's close-range finish (17), before a period of chaos and confusion at Anfield both before and after Glenn Murray put Brighton ahead.
Liverpool: Alisson (7), Alexander-Arnold (8), Van Dijk (7), Matip (7), Robertson (7), Wijnaldum (7), Henderson (7), Fabinho (7), Salah (6), Mane (8), Origi (6)
Subs: Milner (6), Gomez (5), Oxlade-Chamberlain (5)
Wolves: Rui Patricio (5), Doherty (6), Bennett (5), Coady (6), Boly (6), Jonny (6), Moutinho (6), Neves (6), Dendoncker (5), Jota (6), Jimenez (5)
Subs: Traore (5), Gibbs-White (5), Vinagre (5)
Man of the match: Sadio Mane
But goals from Sergio Aguero, Aymeric Laporte, Riyad Mahrez and Ilkay Gundogan put City in command, while at Anfield, Liverpool were fending off a dogged Wolves, who should have equalised through Matt Doherty and Diogo Jota.
Mane headed home a second late on (81) to wrap up a victory, and the home fans gave Liverpool a huge ovation at full time as attention now turns to the Champions League final against Tottenham on June 1. Wolves finish seventh, meaning they will play in Europa League qualifying from July 26 if Manchester City win the FA Cup final on Saturday against Watford.
Liverpool were ahead following an untidy opening quarter of an hour as Trent Alexander-Arnold paced down the right before seeing his deflected cut-back fall into the path of Mane, and the Senegalese forward made no mistake to strike past Rui Patricio.
Liverpool were top, and after Andrew Robertson stung the hands of Rui Patricio from range, there was 21 minutes of bedlam at Anfield. First, misinformation of a Brighton goal saw Anfield celebrating prematurely, before Murray did indeed Brighton ahead, prompting pandemonium in the stadium.
But it did not last long as Aguero and then Laporte put City in command, and it could have been even worse for Liverpool had Matt Doherty's effort from the right of the box not hit the bar and gone over Alisson's goal.
Wolves pushed for a leveller, but Anfield was flattened by a goal elsewhere as Mahrez put City 3-1 up on the south coast, as Divock Origi saw a gilt-edged chance blocked superbly by Conor Coady.
Jota saw a one-on-one chance denied by Alisson at the other end, but Liverpool put the game to bed just after City had done the same through Gundogan's free-kick, as Mane got on the end of another Alexander-Arnold delivery to head in from close range.
Mane finished the season on 22 goals, sharing the top spot in the Premier League top scorer charts with team-mate Mo Salah and Arsenal's Pierre-Emerick Aubameyang, while Alexander-Arnold's 13 assists is the most by a defender in Premier League history.
⚽️ Aubameyang— Sky Sports Premier League (@SkySportsPL) May 12, 2019
It is a three-way tie for the Premier League Golden Boot
Virgil van Dijk headed an Alexander-Arnold corner against the bar moments later, but it ended 2-0 as an unforgettable domestic season ended without the ultimate domestic prize for Jurgen Klopp's side.
Liverpool could not have done more to win this Premier League title and this team can grow. was tough for the Anfield crowd to take but these supporters have every reason to believe in Jurgen Klopp's team, writes Adam Bate.
"People might say we could have done this or that but not really, I don't think [we could have done any more]. City were lucky in moments, we were lucky in moments. It was about staying in the race and believing and that's what we did.
"When your opponent is City, it's difficult. They couldn't get rid of us and we couldn't get rid of them. Being second in the Premier League is not what I wanted but we have to see it as the first step for this team. We have three weeks to prepare for the Champions League final - let's give it a go."
- Liverpool became the first team in top-flight history to win as many as 30 games and 97 points in a season and not win the title.
- No side has ever previously lost just one game in a top-flight season and not won the title - the previous record was also held by Liverpool in the 2008/09 season (two defeats, finished 2nd).
- Liverpool's tally of 97 points would have been enough to win the Premier League in all but one of the previous 26 seasons of the competition (2017/18).
- Wolves have ended the season in 7th position - the highest by a newly-promoted side in the Premier League since Ipswich Town finished 5th in 2000/01.
Man of the match - Sadio Mane
Mane continued his fantastic finish to the season with both goals, securing a share of the Golden Boot award in the process. He didn't have many other sights of goal but was clinical with the two chances that came his way.
Liverpool go to Madrid for the Champions League final against Tottenham on June 1, kick-off at 8pm. Here's how you can follow the match on Sky Sports.