The strong form of Luis Diaz has also pushed Minamino further down the pecking order at the club, although he still managed 10 goals and one assist in 24 appearances across all competitions last season.
However, Minamino only made 11 appearances in the Premier League - 10 of which came as a substitute - and he was left out of the squad entirely on 11 occasions.
The Japan international played just 176 minutes in the top flight last season, and with his contract due to expire in two years' time, Liverpool are expected to try to garner a fee for him this summer.
A fee of £17m would supposedly be required to prise the Japan international away from Liverpool, and he has also been linked with a move to Leeds United as part of a deal for Raphinha.
Whites boss Jesse Marsch briefly worked with Minamino during their time together at Salzburg and is said to be keen on a reunion, but Liverpool are no longer expected to move for Raphinha this summer as they prepare to complete their transfer business early.
Minamino's only Premier League start in 2021-22 saw him play the full 90 minutes and find the back of the net against former loan club Southampton, and Klopp admitted that it was a "crime" for the attacker to remain on the fringes of the team for so long.
"Takumi Minamino, it's a crime he's not playing more often. It's a crime! I apologise! Crazy! People ask me if it's hard to pick a line-up," Klopp told a press conference.
"No, that's fine. I love it! I have options. Today we could have lined up differently, but we really liked it. The football we could play was really good. It's hard [to leave people out].
"I expect them to react like they do, but it's not normal. It's special. Whatever happens, happens because the group is pretty, pretty special. It was like 'Wow, these boys!' It's like having Ferraris in the garage and then you let them out and they play like this."
Minamino is seemingly set to leave Liverpool having registered 14 goals and three assists in 55 outings for the Reds, winning the Premier League, FA Cup and EFL Cup in the process.
Divock Origi and Loris Karius's exits have already been confirmed, and Minamino could be joined out of the exit door by Alex Oxlade-Chamberlain, whose own deal runs out in 2023, as well as Nat Phillips and Neco Williams.