He either doesn't like to press or is simply unable to as much as Klopp would like, perhaps because his body just can't handle the physical demands that is required of a Klopp team. It won't work for him under Klopp and he'll definitely be gone at some point.
Firminio may not be as good as a finisher or natural goal scorer like Sturridge, however, he runs all day long and has a huge appetite for closing down. He allows Liverpool to start off the press from the front, watching that United game encapsulates his importance to the side, he was pushing United back and forcing them to make mistakes for the whole game. Not only that but he was anticipating the mistakes and positioning himself to be a contstant thorn in their side.
With that said they do lose something with someone like Sturridge on the bench, there was a chance in that United game that fell to Firminio that Sturridge would have put away 9/10. However, for the particular brand of football Klopp plays he's almost a perfect player.