It was Palace's seventh straight loss and they can now finish no higher than 14th on the Premier League table.
And Hodgson has blamed his lack of squad depth for his team's performances.
"The lack of strikers we have and lack of goalscorers that has been a constant theme for the whole of the three seasons I've been at the club so nothing changes," he told Match of the Day.
"You mustn't forget in these recent matches we have played some of the top teams in the country and we are doing it with a weakened team.
"I don't know what more we can do. I can't magic players out of thin air. We have the squad we have. We are not going to recover any of the injured players, it will be putting out the same players today on Sunday who are really tired and giving their all for the club.
"We just have to get on with and make certain not to allow what has happened in this period to affect next season."