Cherries are now on their worst losing run since promotion to the top flight, with losses against Newcastle, Wolves, Tottenham and Crystal Palace, as well as the setback against the Reds.
Howe said: “I don't want to make the excuses of injuries behind everything, but if you just look at the number we have, with the quality of players we are missing, I'm not sure there's many Premier League teams that could cope with that.
“The trouble is it's difficult for me to give good news and say 'well, we are going to get a load back in a couple of days' because I'm not sure that's going to happen.
“But we have to find a way. It's probably the biggest challenge we have faced since coming into the Premier League, with what we had thrown at us in our first season.
“But I think this is going to be the biggest challenge."