Philip Billing hit a shot straight at Guaita at the end of the first half, while Dominic Solanke just failed to connect with a risky low ball shortly after the restart.
"There's no hiding place at this level, it is so tough and so hard, but the only way you will get there is with the collective and as a group now we have to come out swinging and come out fighting", Howe said.
Hodgson added: "Where we have been strong strangely enough is centre-back and blow me down we lose Gary before Burnley, Scott during the Burnley game and in this game we lose another centre-back".
Bournemouth wanted to be down the other end of the pitch in their attempts to end a run of three straight defeats, but Palace put them on the verge of four with 14 minutes left at Selhurst Park.
Schlupp then scored the victor after he raced past Jefferson Lerma and Dominic Solanke before dribbling into the area and rifling an effort past Aaron Ramsdale from 12 yards out.