The Eagles lost 3-0 at Villa Park on Boxing Day despite playing the whole second half with a man advantage after Tyrone Mings was sent off.
It is now two consecutive defeats for Palace and 10 goals conceded in those games without scoring a goal and Hodgson has come in for criticism for supporters.
Hodgson and the team must now regroup for the visit of Leicester on December 28, and the manager feels it is a good thing that the players do not have time to dwell on their defeat.
“I don’t think it would have been a good thing for us to dwell on it any longer than we had to,” said Hodgson.
“But I do think we have to analyse it, we have to look ourselves in the mirror and ask ‘what have we done wrong? What could we have done to prevent this?’ We are going to have to make certain that we find out a way around that and try to prevent it happening again in two days’ time.”
Palace were behind inside five minutes and Hodgson feels that knocked the stuffing out of his side on Boxing Day.
“We all know in the Premier League how important the first goal is,” said the 73-year-old. “If you can get it, it can give you a considerable edge. Recently we’ve been conceding early goals.”