The 25-year-old is expected to be on the sidelines for the next six weeks after picking up a hamstring injury while on international duty with Senegal earlier this week.
The Reds are already without Adam Lallana and Nathaniel Clyne due to injury, and while Klopp admitted that the Mane setback is "not cool", he is adamant that his side are "in a quite comfortable situation".
"Things like this happen. If you look around the world, a lot of players in this international break got injured," Klopp told the Liverpool website. "You always hope that nothing will happen, but as long as they are not around, we don't know exactly what happens. It's quite difficult to get in touch with all the different FAs and all that stuff like this.
"I had a chat immediately after the game with Sadio, how I always do with the boys. It was not clear it would be that serious, but he said 'I feel something in my hamstring', so it was clear it would be at least close for the United game - and now we know it's much longer.
"That's not cool, but we have to deal with it – how we always have to do.
"In the moment, we are still in a quite comfortable situation because we have different options and that's good. That's what we wanted to have before the season – now we have it and now we have to use it."
Mane has scored three goals in five league appearances for Klopp's side so far this season, helping them up to seventh in the Premier League table ahead of tomorrow's blockbuster clash with Manchester United at Anfield.