The Reds were top for 21 first-half minutes, only for Manchester City to recover from falling behind at Brighton to record a convincing 4-1 victory.
Sadio Mane scored from close range after 17 minutes and again after 81 to join Liverpool team-mate Mohamed Salah and Arsenal's Pierre-Emerick Aubameyang as the Premier League's top scorer on 22 goals.
Liverpool keeper Allison was confirmed as the Golden Glove winner with 21 clean sheets
The victory was Liverpool's ninth in a row and their 30th overall. They finished on 97 points, the third-highest top flight total in English football history.