Monk admitted he was "gutted" by the news, but has backed the board to bring in the right man as the club prepare for next season.
He told Sky Sports: "He's a top, top manager and we are very disappointed to lose him. He's honest, treats us like adults and knows his football.
"His philosophy, views and training are inventive. We never do the same session more than twice and that makes it exciting.
"I think every manager is different but I think he's got the ingredients to be a top, top manager.
"As much as we are gutted to lose him he's earned the right to work for a club like Liverpool. He deserves this chance.
"There will be many names linked with the job but it's important for the board to pick the right man. We're a close knit club. Everyone sticks together so we'll have to do that again."