Klopp and Wagner’s relationship goes back a long way, with the latter best man at the Liverpool manager’s wedding, having played together at Mainz.
That made Sunday’s meeting at Anfield all the more poignant, as the first game since the announcement that Klopp would leave the club in the summer.
It ended in a resounding 5-2 victory for the Reds – as many expected beforehand, with Wagner even joking that he lost “like always!”
“We saw each other before the game, together in the stadium, probably we’ll see each other after as well,” he told reporters after the game.
“Fine to see him, because normally I would not have seen him before the summer.
“I think the last time I saw him was in the summer as well, so this draw gave us a chance. This is something personal, which is quite nice, about this game as well.
“He wanted to win, I wanted to win, so we gave ourselves and the teams a go. I lost, like always!”
Asked whether he was shocked to hear that Klopp would be leaving Liverpool, Wagner denied, with the belief being that he was among those told beforehand.
“No, I was not shocked. I was not shocked,” he explained.
“To be fair, I think a lot of people said a lot of things about his decision and his announcement; everything that we have spoken about is super private.
“This is why I don’t really like to answer questions about his decisions and my thoughts about it. I think we should all respect what he has done.
“Now I wish him, really, from the bottom of my heart, to the end of the season, the very best, that he is as successful as he can be with this team. Nobody knows what this means.”
Speaking to BBC Sport, Wagner continued: “I think he got everything that he deserved.
“I think this goodbye tour in English football will be a great one for him and hopefully with a lot of success.”
And on Liverpool’s chances of a quadruple to mark Klopp’s exit, he German added: “He says it’s nearly impossible and if he says it’s near impossible, I will say the same.
“But nearly impossible means not impossible so I think he and everyone else knows exactly how difficult it is.
“I would love now to see how they compete and nobody knows what will happen.”