Klopp's men, who were on course to give their manager a fairytale ending before a string of bad results last month derailed their title challenge, finished the season on 82 points, nine behind winners Manchester City and seven behind third-place Arsenal.
"I've got no words, it's a very emotional day," Liverpool captain Virgil van Dijk told Sky Sports while fighting back tears. "It was always going to be a tough afternoon. We wanted to make sure that we do our job basically and then obviously we can all be very emotional after the game.
"[Klopp] deserves every bit of love that he's getting."
Wolves were reduced to 10 men in the 28th minute when Nélson Semedo was sent off for his ugly tackle on Mac Allister. Six minutes later, the Argentina midfielder headed home Harvey Elliott's curling cross, bringing Klopp to his feet with a huge smile. Quansah doubled Liverpool's lead in the 40th minute when he poked in Liverpool talisman Mohamed Salah's shot.
Klopp bade farewell to the Anfield faithful -- including owners John Henry and Tom Werner, who flew in from Boston for the occasion -- having won 305 matches (including penalty shootouts) with the club.
A crowd more than a dozen deep and bathed in red smoke squeezed shoulder to shoulder along the road leading into Anfield on Sunday to welcome the team busses as they pulled in pregame.
If Liverpool's pregame singing of "You'll Never Walk Alone" -- a song by 1960s Liverpool band Gerry and the Pacemakers, which became the club anthem -- raises goosebumps most games, the Anfield crowd sang at the top of their lungs on Sunday while Klopp raised a hand to his heart.
"This morning I woke up and I was completely in game mode," Klopp told Sky Sports before kickoff. "We had a normal team meeting and the 60,000 here and the few million watching deserve that.
" call it the last dance, so let's dance!"
Klopp has won seven trophies since joining the club in 2015, including the Champions League in 2019 and Liverpool's first English League title in three decades in 2020. He also won the Club World Cup, FA Cup, League Cup twice and UEFA Super Cup, as well as the Community Shield.
But the German was beloved as much for his passionate demeanour as his on-field success with the Merseyside club. He delighted fans with his high-octane goal celebrations and his post-victory fist pumps. He wrapped his players in huge bear hugs.