Whether the cameras simply missed him doing so or whether there was another reason behind his apparent lack of involvement was unclear.
Núñez began Sunday’s game on the bench, having not started a match since Liverpool’s 2-0 defeat at Everton last month which all-but ended their hopes of ending Klopp’s reign with the Premier League title.
The £85 million signing, whose frustrating Anfield career was summed up in the Merseyside derby loss, embraced Klopp after coming on against Wolves with the match virtually won.
Some of Klopp’s other players, notably Trent Alexander-Arnold, were in tears after Sunday’s game as the magnitude of the occasion sunk in.
Addressing the crowd, Klopp said: “I’m completely surprised. I thought I’m already [going to be] in pieces, to be honest, but I’m not. I’m so happy, I can’t believe it.
“I’m so happy about you all, about the atmosphere, about the game, about being part of this family, about us, how we celebrated this day. It’s just incredible. Thank you so much.
“Honestly, for whatever reason, it doesn’t feel like an end. It just feels like the start, because I saw today a football team playing full of talent, full of youth, full of creativity, full of desire, full of grit.”
He added: “I’m one of you now. I love you to bits. On my jumper is ‘Thank you Luv’ and ‘I will never walk alone again’. Thank you for that! You are the best people in the world. Thank you!”