The 70-year-old replaced Frank de Boer in the Selhurst Park dugout on Tuesday but could not deliver an instant turnaround in fortunes as Palace became the first side in top-flight history to lose their first five games without scoring a goal.
Palace now face a daunting fixture list that sees them face Manchester City, Manchester United and Chelsea in their next three league games, and Hodgson has warned that things may get worse still before they get better.
"It is five defeats, zero points and a really tough programme ahead if you look at the quality of the opponents," he told reporters. "So, it's painful today, and I fear it is going to be painful in some of the moments going forward.
"But there is no way you can talk yourself out of that and there is no point in making bold statements that might not be ratified in some way.
"We have just got to get down to working with the players, deciding which ones are the best ones to get us out of trouble."
Palace face some respite from league action when they welcome Huddersfield Town in the EFL Cup on Tuesday night, before heading to the Etihad for their next league game next Saturday.