The club released a statement confirming the injury news on Friday and Klopp added that Firmino might be unavailable until December.
"Losing Bobby Firmino is a blow," Klopp told a news conference."I don't think I need to say how big it is. It's a serious injury.
"We talk about weeks -- more than four I consider as a serious injury. Then we have to see. Bobby is a quick healer."
Following a disappointing draw against Brighton last week, Liverpool are third in the table and five points behind leaders Chelsea.
However, Klopp added that Liverpool don't see themselves as underdogs in the title race.
"We don't consider ourselves in that way -- we want to be in it, but whatever role we have I don't care," he said. "With our quality we should be in and around the top of the table.
"We don't have to talk about quality of [Manchester] City and Chelsea. The league is incredible. There's no game where you can go and say 'we can rest him and him and him'. In the last two or three years, it has been the best league in the world."