Juergen Klopp's men also have a Champions League final against Real Madrid to look forward to next weekend in Paris where they could win their seventh European Cup.
"The lads have given everything, so you can't have too many issues. We've given absolutely everything all season, right until the last day, and in January we'd have bit your hand off to take it to the last day," Liverpool captain Jordan Henderson, who lifted his side's first Premier League trophy in 2020, told Sky Sports.
"We're a bit disappointed today. We've got to say congratulations to City, of course, and then focus on the match next week."
Wolves took a shock lead three minutes in when defender Ibrahima Konate misjudged a bouncing ball from a goal kick allowing Raul Jimenez to run in behind on the right and pick out Neto to side-foot in his first goal of the season.
Liverpool equalised in the 24th minute when a cute Thiago Alcantara backheel set Mane free to charge at goal and strike an effort that was so fierce, goalkeeper Jose Sa could only get a hand to it before it went in.
Sa had to be replaced by John Ruddy at halftime due to an injury and soon after Liverpool brought on Salah, rested from the beginning, in search of the winner and peppered shots at goal, only to see them continually blocked by Wolves defenders.
The atmosphere became frantic as news filtered through from the stands that City were losing 2-0 to Villa and the title would end up at Anfield if Liverpool could find a goal.
They found that breakthrough seven minutes from fulltime when Salah squeezed in a loose ball in the box. The goal was the Egyptian's 23rd of the season and meant he finished the campaign level as top scorer with Tottenham Hotspur's Son Heung-min.
Full back Andy Robertson then put the gloss on the scoreline late on by sliding in Roberto Firmino's cutback.
However, by that time City had completed their own comeback win over Villa, meaning they retained the title and Liverpool finished the season as runners-up. Wolves finished 10th on 51 points.